Form Of Differential Equations Research Articles

Dynamic processes of quartic autocatalysis chemical reaction in Williamson nanofluid flow over a parabolic surface

Studying the dynamic processes of quartic autocatalysis chemical reactions in Williamson nanofluid flow over a parabolic surface is significant for optimizing and enhancing the efficiency of industrial and engineering systems involving complex fluid dynamics and chemical reactions. The investigation of the type of flow channel is very important. In the present problem, the motion is investigated on an upper horizontal surface of a paraboloid of revolution. The analysis is performed about the Williamson nanofluid flow with Cattaneo–Christov (C–C) heat flux, quartic autocatalysis chemical reaction and gyrotactic microorganisms motion past an upper horizontal surface of a paraboloid of revolution (uhspr). Similarity transformations are applied to get the non-dimensional equations in differential form. Homotopy Analysis Method (HAM) is operated for computing the solution. The solution is processed to obtain the results which have been shown through the graphs which note the effects of existing parameters on profiles. The computed results have a nice agreement with the published results. The investigations are about the upper horizontal surface of a paraboloid of revolution which has leading role in science, aerodynamics like surface of a rocket, bonnet of a car and pointed surface of a vehicle and airplane.

Numerical simulation of heat transport mechanism in chemically influenced ternary hybrid nanofluid flow over a wedge geometry

Ternary hybrid nanofluid flow over a wedge surface facilitates optimization, promotes industrial processes such as heat transfer, temperature regulation, material compatibility, energy efficiency and is very useful in equipment design. Due to this attention the current study focalizes the heat diffusion and mass transportation in ternary hybrid (TiO2-AL2O3-SiO2) nanofluid flow over a stretching/shrinking wedge geometry. Additionally, Ternary hybrid flow is examined under the impact of activation energy together with chemical reactions. The nanofluid flow process is structured using Modified Boungiorno Model together with framed set of partial differential equation (PDEs). The resulting systems is altered into non dimensional form of ordinary differential equation (ODEs) using transform functions and linearization is obtained through shooting technique. MATLAB bvp4c solver scheme is utilized for numerical findings of the problem. Influence of key parameters are analyzed on velocity, temperature, and concentration field. Fluid concentration intensifies via augmentation in activation rate whereas wedge stretching due to larger values of wedge angle, lessens velocity of fluid. Heat transportation escalate with higher values of fluid index, whereas negative trend is seen in case of higher value of Brownian parameter.

A one‐dimensional phenomenological constitutive model of shape memory alloys considering the cyclic degradation of two‐way memory effect

AbstractThis study introduces a one‐dimensional phenomenological constitutive model designed to describe two‐way shape memory effect (TWSME) and its associated cyclic degradation. The model utilizes the logistic function to formulate the phase transformation equation, incorporates the expansion of key parameters into their respective fatigue functions to characterize the fatigue phenomenon, and integrates a phase transformation rate regulation function into the differential form of the phase transformation equation. This integration facilitates the control over the entire phase transformation process and the simulation of incomplete transformations. The model is distinguished by its comprehensive functionality, simple form, ease of calculation, and the clear and direct influence of key parameters. Furthermore, it offers a degree of flexibility because each function within the framework is replaceable. The simulation of the TWSME strain and recovery stress hysteresis loop deformation has been successfully conducted, enabling the description of internal hysteresis loops caused by incomplete transformation. The validity of the model is corroborated by comparing it with existing experimental results.

Modeling of dynamic bubble deformation and breakup in T-junction channel flow

Bubble deformation and breakup due to strain-rate-induced stress is investigated for a laminar flow configuration. The bubble shape is assumed to be a prolate ellipsoid. A new model for bubble deformation under dynamic load is introduced in the form of an ordinary differential equation for the deformation energy. Breakup is identified with a critical value of the deformation. As an application case, the flow in a joining T-junction is considered with the ratio of the volume flow rate being unity and the outflow Reynolds number being 1800. Dilute, dispersed bubbles with a diameter of 0.5 mm are injected. High-speed shadowgraphy is used and bubble parameters are evaluated via image processing. The capillary number is obtained from a single-phase flow simulation providing the instantaneous shear rate at the position of the bubble. The deformation resulting from the proposed model is then compared with the measured deformation for an exemplary bubble trajectory.

Implementing the predictor-corrector approach to examine the thermo-solutal convection for buongiorno eyring-powell nanofluid model with squeezed microcantilivier surface

The Buongiorno nanofluid model serves as a foundational model for theoretical and experimental research in the field of nanofluids, and this model can be applied to various engineering problems, including heat exchangers, biomedical applications, solar collectors, nuclear reactors, and different cooling systems in the automotive and electronics industries. The use of nanofluids in the Eyring-Powell fluid over a squeezed sensing surfaces is a vital area of research for the design and improvement of microfluidic devices and sensors, which find widespread usage in industrial and medical applications. The main purpose of this work is to note the augmentation in thermal conductivity by using the Buongiorno nanofluid model along with the natural convective flow of non-Newtonian Eyring-Powell fluid that is moving on the squeezed sensory surface along with slip velocity. The viscosity of a fluid is assumed to be dependent on temperature. The Cattaneo-Christov heat and mass flux and chemical reaction are assumed to determine the combined effect of heat and mass transport. The governing model of equations is in the form of dimensional partial differential equations, and we have to convert these equations into ordinary differential equations; therefore, a set of similarity transformations is adopted for making the equations into dimensionless form. The numerical results were obtained by adopting the predictor and corrector multistep method, namely the ‘Adams-Bashforth’ technique, in Matlab software. The use of natural convective flow enhances the velocity region. The velocity slip parameter increases the velocity of the fluid, whereas the viscosity parameter drops the velocity profile. The thermophoresis and Brownian motion parameters are the sources of the increment in the temperature region. The thermal relaxation and solutal relaxation parameters are the sources of decline in the temperature region. The squeezing parameter is the source of reduction in the skin friction, whereas the result indicates that the fluid parameter, Grashof number, and viscosity coefficients increase the skin friction.

Stochastic neuro-swarming intelligence paradigm for the analysis of magneto-hydrodynamic Prandtl–Eyring fluid flow with diffusive magnetic layers effect over an elongated surface

In recent years, the integration of stochastic techniques, especially those based on artificial neural networks, has emerged as a pivotal advancement in the field of computational fluid dynamics. These techniques offer a powerful framework for the analysis of complex fluid flow phenomena and address the uncertainties inherent in fluid dynamics systems. Following this trend, the current investigation portrays the design and construction of an important technique named swarming optimized neuro-heuristic intelligence with the competency of artificial neural networks to analyze nonlinear viscoelastic magneto-hydrodynamic Prandtl–Eyring fluid flow model, with diffusive magnetic layers effect along an extended sheet. The currently designed computational technique is established using inverse multiquadric radial basis activation function through the hybridization of a well-known global searching technique of particle swarm optimization and sequential quadratic programming, a technique capable of rapid convergence locally. The most appropriate scaling group involved transformations that are implemented on governing equations of the suggested fluidic model to convert it from a system of nonlinear partial differential equations into a dimensionless form of a third-order nonlinear ordinary differential equation. The transformed/reduced fluid flow model is solved for sundry variations of physical quantities using the designed scheme and outcomes are matched consistently with Adam's numerical technique with negligible magnitude of absolute errors and mean square errors. Moreover, it is revealed that the velocity of the fluid depreciates in the presence of a strong magnetic field effect. The efficacy of the designed solver is depicted evidently through rigorous statistical observations via exhaustive numerical experimentation of the fluidic problem.

Collisional breakage population balance equation: An analytical approach

This work presents a unique semi-analytical approach based on the homotopy analysis method (HAM), called accelerated HAM, recently proposed in (Hussain et al., “Semi-analytical methods for solving non-linear differential equations: A review.”, JMAA, 2023), to solve the collisional breakage population balance model, which is an integro-partial differential equation. We compare our findings with those obtained using the Adomian decomposition method, a well-known technique for solving various forms of differential equations. By decomposing the non-linear operator, we investigate how to utilize the convergence control parameter to expedite the convergence of the HAM solution towards its precise value in accelerated HAM. The other objective of the article is to examine the theoretical convergence analysis of the two proposed methods. Additionally, we conduct theoretical research on the error estimates for both the techniques. To validate our schemes, several numerical examples are considered and the numerical simulations demonstrate that the suggested techniques provide accurate estimates for the solution and moments of the collisional breakage equation.

Fixed‐time adaptive event‐triggered fault‐tolerant control of nonlinear systems with actuator failures

AbstractThe problem of fixed‐time adaptive event‐triggered fault‐tolerant control (FTC) is investigated for a class of nonlinear systems with actuator failures in this paper. Firstly, by utilizing back‐stepping algorithm and the fixed‐time stable criterion, a novel fixed‐time adaptive fault‐tolerant controller and parameter updated laws in forms of nonlinear differential equations are developed to counteract actuator faults and parameter uncertainties in fixed time. Then, the event‐triggered mechanism based on the relative threshold method is applied to the proposed control scheme to save network resources. Furthermore, by the Lyapunov stability theory, it can be proven that all the closed‐loop signals of system remain bounded, and the tracking error converges into a small neighborhood of the origin within fixed time interval. Finally, the simulation examples are shown to verify the feasibility and efficiency of the presented strategy.

Numerical Simulation of Bioconvection Maxwell Nanofluid Flow due to Stretching/Shrinking Cylinder with Gyrotactic Motile Microorganisms: A Biofuel Applications

The bioconvection effects with nanofluid are major application in biofuels. This analysis aimed to observe the bioconvection effect in unsteady two-dimensional Maxwell nanofluid flow containing gyrotactic motile microorganisms across a stretching/shrinking cylinder evaluating the consequences of thermal radiation and activation energy. The Cattaneo-Christov double diffusion theory is also observed. Nanofluids are quickly perceptive into many solicitations in the latest technology. The current research has noteworthy implementations in the modern nanotechnology, microelectronics, nano-biopolymer field, biomedicine, biotechnology, treatment of cancer therapy, cooling of atomic reactors, fuel cells, and power generation. By using the proper similarity transformation, the partial differential equations that serve as the basis for the current study are gradually reduced to a set of highly nonlinear forms of ordinary differential equations, which are then numerically, approached using a well-known shooting scheme and the bvp4c tool of the MATLAB software. Investigated is the profile behavior of the flow regulating parameters for the velocity field, thermal field, and volumetric concentration of nanoparticles and microorganisms. From the results, it is concluded that velocity is reduced with a larger bioconvection Rayleigh number. The thermal field is increased with a larger amount of thermal Biot number and thermal radiation. The concentration of nanoparticles increases with an increment in the thermophoresis parameter. Furthermore, the microorganism’s field is decreased with a larger Lewis number. The findings demonstrate that by optimizing the concentration of nanoparticles and microorganisms, the thermal efficiency of biofuels can be significantly improved. This leads to more sustainable and efficient energy production. By optimizing the concentration of nanoparticles and microorganisms in biofuels, the thermal properties can be significantly improved, leading to more efficient combustion processes. This can reduce the overall cost and increase the yield of biofuels. Improved cooling systems for medical imaging devices such as MRI machines can be developed using nanofluids, ensuring better performance and patient safety.

The Properties of the Physical Parameters in the Triple Diffusive Fluid Flow Model

The existence of more than one diffusive component in fluid mixtures is observed in these situations: underground water flow, the mechanism of acid rain, the existence of contaminant in some certain mixture, etc. These diffusive components are occurred with the single temperature gradient (since all of the elements are dissolved into the same mixture) and 2 types of concentration gradients (since the dual diffusive components are dissolved in the same mixture). Besides, many industrial and engineering processes are utilizing the concept of convective fluid flow especially over a shrinking sheet. Therefore, a mathematical model for triple-diffusive flow over a nonlinear compressing sheet has been developed in this paper, and subjected to the Soret-Dufour effects. The model comprises of five initial equations namely continuity, momentum, energy, concentration of component 1 and concentration of component 2 equations, together with boundary conditions. These initial equations are expressed as partial differential equations. However, the finalized equations are in the form of ordinary differential equations. Later, the bvp4c programme provided by the Matlab Software is used to solve the ordinary differential equations and the boundary conditions. Three distinct values of each governing parameter are fixed into the bvp4c function, to observe the behaviour of the physical parameters, namely as local Nusselt number and local Sherwood number. The main finding of the dual numerical solutions varies for increasing governing parameters until they intersect at the critical points. In conclusion, the governing parameters affects the heat and mass transfer of the fluid flow model model.

Abundant Soliton Solutions to the Generalized Reaction Duffing Model and Their Applications

The main aim of this study is to obtain soliton solutions of the generalized reaction Duffing model, which is a generalization for a collection of prominent models describing various key phenomena in science and engineering. The equation models the motion of a damped oscillator with a more complex potential than in basic harmonic motion. Two effective techniques, the mapping method and Bernoulli sub-ODE technique, are used for the first time to obtain the soliton solutions of the proposed model. Initially, the traveling wave transform, which comes from Lie symmetry infinitesimals, is applied, and a nonlinear ordinary differential equation form is derived. These approaches effectively retrieve a hyperbolic, Jacobi function as well as trigonometric solutions while the appropriate conditions are applied to the parameters. Numerous innovative solutions, including the kink wave, anti-kink wave, bell shape, anti-bell shape, W-shape, bright, dark and singular shape soliton solutions, were produced via the mapping and Bernoulli sub-ODE approaches. The research includes comprehensive 2D and 3D graphical representations of the solutions, facilitating a better understanding of their physical attributes and proving the effectiveness of the proposed methods in solving complex nonlinear equations. It is important to note that the proposed methods are competent, credible and interesting analytical tools for solving nonlinear partial differential equations.

Hydrothermal properties with entropy generation effects on a hybrid nanofluid considering thermal radiation on a stretching/shrinking sheet

Heat transfer efficiency is a significant area of modern research because it is used in a variety of engineering domains, improving the performance of thermal systems such as solar collectors. In this article, a statistical optimization of hybrid nanofluid flow through a stretching/shrinking inclined surface inside the solar-powered ship with entropy generation is investigated by utilizing copper and alumina as a tinny-sized nanomaterial in base fluid water. Copper is also corrosion-resistant with a high thermal conductivity that can be useful in marine environments where salted water and humidity damage the other materials. Coating or a catalyst for solar thermal systems aluminum oxide can be utilized to generate steam or hot water by using the heat coming from the sun. The significance of thermal radiation is considered as the heat source. The developed mathematical model in the form of the partial differential equation is transformed to nonlinear coupled Ordinary Differential Equations (ODEs) by using similarity variables. The reduced equations are solved numerically by applying the shooting algorithm with the bvp4c tool of MATLAB. The surface response methodology is utilized for the statistical optimization of experimental design parameters. The entropy generation rises with the increase of Reynolds number and Brinkmann number. The highest entropy value is found for the Cu-Al2O3/water with λ = 1.0 for Re = 15 and Br = 15. No significant change is reported in the local Nusselt number for changing the Eckert number value. The Response Surface Modeling (RSM) result shows that the experimental input parameter rises with “a factor.”

Physics-Informed Machine Learning for Structural Damage Diagnosis in Aluminium Plates

Damage diagnosis plays a crucial role in Structural Health Monitoring (SHM) by facilitating the identification, localization, and estimation of the extent of defects in structures. Lamb waves, known for their sensitivity to defects, are widely employed in SHM methods for thin-walled structures. Most of those traditional methods require extracting damage indices from Lamb wave signals. This operation involves substantial post-processing and implies that part of the diagnostic information is lost. To solve those limitations and improve the damage diagnosis accuracy, machine learning methods have recently been proposed in the literature. However, the reluctance of the industrial sector to adopt conventional black-box models due to their lack of explainability poses a challenge. This study proposes a physics-informed machine-learning approach to address the limitations of standard black-box methods. Particularly, a Physics-Informed Neural Network (PINN) is implemented to predict the density of an aluminium plate based on measurements of plate displacements caused by Lamb wave excitation. This is made possible by the implementation of a specific loss function, which leverages physical knowledge in the form of the partial differential equation governing Lamb waves. Predicting the plate density based on measured displacements eliminates the need for artificial damage indices, utilizing the density variation itself to detect and localize damage. Additionally, the outputs of the PINN, rooted in physics equations, offer enhanced explainability compared to standard black-box models. The versatility of this framework extends to predicting material properties distributions for components, and efforts will be directed towards adapting the method for composite materials, where the approach may pose additional challenges.

Advanced Innovations in Electronic Control Units: Enhancing Performance and Reliability with AI

This paper proposes a methodology for the design of electronic control unit (ECU) hardware units with increased performance and reliability. Today's vehicles are equipped with dozens of ECUs that significantly influence the system's efficiency, reliability, performance, and safety. With the increased complexity of control algorithms and the environmental constraints that automotive systems operate, the robustness and efficiency of the ECUs are of utmost importance. In this work, an approach is proposed based on combining hardware redundancy, commercial field programmable gate arrays (FPGAs), and artificial intelligence strategies to provide increased redundancy checks and robust control. An additional redundancy is added to the hardware architecture of the ECU to include a parallel hardware unit. The two controlling units operate in parallel. The output of each of them is compared, allowing redundancy checks in the computation of the output variable (oV) of the system. The mathematical model of the ECU depicts the governing equations of the ECU in the form of differential equations, which results in a corresponding state-space configuration. These mathematical models are encoded into the field programmable gate array (FPGA) and processed in hardware, leading to an equivalent software-based implementation. To analyze the performance of both models within the ECU, an artificial neural network (ANN)-based strategy is proposed. The ANN depicts the governing equations of the ECU in the form of differential equations encoded in the form of sigmoidal functions. To analyze the reliability of the control action in the ECU, the temperature of the system is increased, which leads to a random variation of the system parameters. The variability of the ECU parameters leads to a deviation in the computation of the oV and the corresponding control action. The robustness of the control is determined in such conditions. A control law is determined to guarantee proper control action under variations in the governing equations of the system. This control law is represented by a simple algebraic equation, which can then be cast in various control strategies, such as look-up tables or fuzzy logic controllers. Several cases are simulated to assess the performance of the proposed control law for the hardware redundancy scheme, for the ANN-based equivalent software implementation approach, and for the additional fuzzy logic controller. The simulation results are analyzed concerning the requested oV and give insight into the performance and reliability of the proposed dedicated ECU design.

Thermal transport characteristics of fluid-particle suspension in a vertical uniform tube: A computational study on Rabinowitsch fluid with uniform heat source

Problem statement The thermal transport of fluid-particle suspension in Rabinowitsch fluid is discussed theoretically in a vertical uniform tube under the consideration of a uniform heat source. Methodology The fluid and particle phase models are used to develop the mathematical model in the form of partial differential equations which are solved through the symbolic software MATHEMATICA version 12.0 and present the exact solution of temperature distribution, velocity of fluid and particle phases, wall shear stress, pressure gradient, pressure rise, and stream function, etc. Computational results and findings The volume fraction density of the particles slows down the motion of the fluid particles. The velocity of Newtonian fluid is maximum as compared to pseudo-plastic and Dilatant fluids. The fluid phase velocity is superior to particle phase velocity distribution for all pertinent parameters of the analysis. The pressure rise increases in the case of Newtonian and pseudo plastic fluid and decreases in Dilatant fluid. The trapping phenomena are strongly associated with the volume fraction density of the particle. The shear stress shows a decreasing trend against the volume fraction density of the particles, Grashoff number, and heat source parameter. Special case The current fluid model (Rabinowitsch fluid) can be reduced in Newtonian, pseudo plastic, and Dilatant fluid for taking κ → 0 , κ < 0 , and κ > 0 , respectively. Applications The current analysis can be useful in biomedical engineering to observe the blood supply through the arteries, the removal of kidney stones, and also the passage of urine to the bladder from the ureter. Originality The present research is original and has not been published before.

Pell Collocation Approach for the Nonlinear Pantograph Differential Equations

Pantograph equations, which we encounter in the branches of pure and applied mathematics such as electrodynamics, control systems and quantum mechanics, are essentially a particular form of the functional differential equations characterized with proportional delays. This study focuses on exploring the approximate solution to the Pantograph differential equation. Since there is no analytic solutions for this equation class, only the approximate solutions can be obtain. For this purpose, Pell Collocation Method which is one of the numerical solution methods is chosen. As the result of applying the method to the equation, an algebraic equation system has been gained and then the approximate solution has been found by using MATHEMATICA via the given initial conditions. The method is applied to the some test examples and then the results are presented by both graphically and by table. The error estimations show that the method works accurately and efficiently.

Creation of a Mathematical Model of a Stationary Rail Circuit in the Form of a Finite Discrete Automaton

Purpose. Ensuring the safety of train traffic is a mandatory task in the development of technical equipment of railway transport in Ukraine. To diagnose and verify the performance of such systems, simulation models of overhead devices, in particular, the rail circle, are used. The most commonly used models are in the form of differential equations and in operator form. Unfortunately, they are not fully suitable for solving this problem. In this regard, there is a need to create a mathematical model that is easier to integrate for checking both relay electrical interlocking and microprocessor-based interlocking systems. Methodology. To achieve this goal, the authors proposed to create a mathematical model in the form of a finite discrete automaton. This paper considers the creation of a model of a station rail circuit as a directed graph. During the creation of the model, the input and output values of the model and the states are determined. The tables of inputs and outputs of the automaton are constructed, sequential expressions for the abstract model of the automaton are created, and their minimization is performed. The states of the automaton are coded using trigger circuits. Findings. In the course of the research, a mathematical model of the rail circle in the form of a Moore model finite automaton was created, and its performance was tested in the Proteus software environment. The developed model allows to simulate the operation of a stationary rail circuit at the level of abstraction, which operates with binary signals. This makes it possible to simplify the coordination of the model with microprocessor-based centralization software. In general, it is now possible to more effectively check the performance of microprocessor-based interlocking systems at the design and commissioning stages. Originality. The developed mathematical model makes it possible to determine the response of the microprocessor-based centralization software to the behavior of the rail circuit in various, in particular atypical, operating modes, as well as to determine the response of the station electrical centralization system to individual failures and to the occurrence of several failures simultaneously. Practical value. The proposed mathematical model can be used both to check the operation of microprocessor-based centralization systems at the design and implementation stages and for relay centralization systems when developing diagnostic complexes for monitoring their performance.

Heat and mass transmission through the nanofluids flow subject to exponential heat source/sink and thermal convective condition across Riga plates

The analysis of the squeezing nanofluid flow across bounded domains received great attention from researchers and engineers due to its tremendous application in automobiles, energy exchangers, and aerodynamics. In the current analysis, we are using double Riga plates parallel to each other, in order to induce the squeezing nanofluids flow with the significances of chemical reaction, thermal radiation, and heat source/sink. The nanoliquid has been prepared by the dispersion of Copper (Cu) nanoparticles (NPs) in kerosene oil (C12H26C15H32) and water (H2O). The nanofluid flow has been modeled in form of nonlinear partial differential equations, which are further convert into the dimensionless form of ordinary differential equations. The obtained set of non-dimensional equations is numerically resolved by using the Matlab built-in package bvp4c. The results are compared to another numerical technique for accuracy purposes. The detailed results are presented in Figures. It has been detected that the energy field of nanofluid is enriched with the effect of heat source/sink component. Moreover, the velocity curve magnifies with the variation of the squeezing parameter of Riga plates, whereas declines with the accumulation of Cu-NPs in both types of base fluid (C12H26C15H32 and H2O).

A parameter estimation method for chromatographic separation process based on physics-informed neural network

Chromatographic separation processes are most often modeled in the form of partial differential equations (PDEs) to describe the complex adsorption equilibria and kinetics. However, identifying parameters in such a model requires substantial computational effort. In this work, a novel parameter estimation approach using a Physics-informed Neural Network (PINN) model is developed and tested for a binary component system. Numerical accuracy of our PINN model is confirmed by validating its simulations against those of the finite element method (FEM). Furthermore, model parameters in the kinetic model are estimated by the PINN model with sufficient accuracy from the observed data at the column outlet, where parameter fitting error can be reduced by up to 35.0 % from the conventional method. In a comparison with the conventional numerical method, our approach can reduce the computational time by up to 95 %. The robustness of the PINN model has also been demonstrated by estimating model parameters from noisy artificial experimental data.

The transition from equations presented in matrix form for the perturbed Earth’s rotation to excitation equations

A convenient method for studying the influence of disturbing factors on Earth’s rotation, such as influence of oceans, atmosphere and hydrology, is representation of the Earth’s rotation equations in the excitation equations form, which was introduced by W. Munc and G. Macdonald. Traditionally, these factors are taken into account in two stages: first, an exact solution is found for an equation of the unperturbed rotation for given Earth’s model, and then the influence of small perturbation factors is taken into account in the form of corrections to the exact solution of unperturbed Earth’s rotation. The equations of unperturbed rotation for most modern theories of Earth’s rotation (and, possible, futures too) can be written in the form of matrix linear differential equations. The purpose of this study is to take into account the influence of small perturbations such as oceans, atmosphere and hydrology on Earth’s rotation in newly created theories of Earth’s rotation. A fairly general algorithm of converting perturbed equations in matrix form to the form of the excitation equations has been developed and presented. As an example, this method was applied to the relatively simple equations of the Sasao, Okubo and Saito theory based on the original Earth’s model of Molodenskii. The equations for finding corrections to the original solution are reduced to the form of excitation equations. The developed algorithm is proposed to be used to transition to equations in the form of excitation in newly created theories of the Earth’s rotation.