Classical Newtonian Mechanics Research Articles

Modeling and analysis of Alpine skiing downhill based on the DPAS model considering four-way inhomogeneous environmental winds with digital twins at downhill course of the Beijing Olympic Winter Games

In Alpine skiing, the influence of the environment wind on the athlete is crucial. To accurately analyze the coupling effect of environment wind speed, wind direction, and the athlete’s skiing process, this paper establishes the kinematic equations of the athlete based on Newtonian classical mechanics and computational fluid dynamics (CFD) and proposes a discretization method for the course. Simulation results were obtained by using CFD to obtain digital twins for the course and its surroundings. The simulation results were also used as input to the wind parameters to analyze the athletes’ sliding performance. The Downhill Process in Alpine Skiing (DPAS) model was constructed to validate the actual downhill course in the Beijing Olympic Winter Games. An analytical framework for downhill skiing with way inhomogeneous winds was demonstrated to be a good simulation and validation of our analytical framework, proving its good simulatability and reliability. The downhill process is also subdivided into four phases: start-up acceleration phase, core acceleration phase, intermittent acceleration phase, and endurance sprint phase, based on the velocity-time curve derived from the actual course simulation. Tactical skiing strategies for skiers to improve their performance are proposed for the different stages of the process. We believe that the DPAS model can also be applied to other parts of Alpine skiing such as slalom, giant slalom, and super-G, and that the results can be used to suggest tactical strategies to improve performance.

Expansive Quantum Mechanical Exploration of Chemical Reaction Paths.

Quantum mechanical methods have been well-established for the elucidation of reaction paths of chemical processes and for the explicit dynamics of molecular systems. While they are usually deployed in routine manual calculations on reactions for which some insights are already available (typically from experiment), new algorithms and continuously increasing capabilities of modern computer hardware allow for exploratory open-ended computational campaigns that are unbiased and therefore enable unexpected discoveries. Highly efficient and even automated procedures facilitate systematic approaches toward the exploration of uncharted territory in molecular transformations and dynamics. In this work, we elaborate on such explorative approaches that range from reaction network explorations with (stationary) quantum chemical methods to explorative molecular dynamics and migrant wave packet dynamics. The focus is on recent developments that cover the following strategies. (i) Pruning search options for elementary reaction steps by heuristic rules based on the first-principles of quantum mechanics: Rules are required for reducing the combinatorial explosion of potentially reactive atom pairings, and rooting them in concepts derived from the electronic wave function makes them applicable to any molecular system. (ii) Enforcing reactive events by external biases: Inducing a reaction requires constraints that steer and direct elementary-step searches, which can be formulated in terms of forces, velocities, or supplementary potentials. (iii) Manual steering facilitated by interactive quantum mechanics: As ultrafast quantum chemical methods allow for real-time manual interactions with molecular systems, human-intuition-guided paths can be easily explored with suitable human-machine interfaces. (iv) New approaches for transition-state optimization with continuous curve representations can provide stable schemes to be driven in an automated way by allowing for an efficient tuning of the curve's parameters (instead of a manipulation of a collection of structures along the path), and (v) reactive molecular dynamics and direct wave packet propagation exploit the equations of motion of an underlying mechanical theory (usually, classical Newtonian mechanics or Schrödinger quantum mechanics). Explorative approaches are likely to replace the current state of the art in computational chemistry, because they reduce the human effort to be invested in reaction path elucidations, they are less prone to errors and bias-free, and they cover more extensive regions of the relevant configuration space. As a result, computational investigations that rely on these techniques are more likely to deliver surprising discoveries.

A Classical Physics Approach for Space Expansion: The Hubble Drift

Accelerating expansion of metric space AEMS is investigated with classical Newtonian mechanics. Relying on earlier positions, the results are analyzed to reveal what could be a new understanding of the theoretical framework of the subject. Notably, it is shown that space is physical; it comprises aggregated waveforms of the chemical elements and shares identical quantization, periodicity and mass-evolution with matter. Three plausible methods are identified for classical investigation of the Hubble effect, all three give same result, Ho= 49.5 km s-1Mpc. AEMS results from coupling of light’s 36.9o tangential component (vr=0.75rω) to periodic space, i.e., a component of the vacuum field’s e-m radiation couples to logarithmically decreasing distance scales, vr(E)/drE, to create an acceleration relative to space not time. Multiplicity of the Hubble constant aHo is traceable to corresponding multiplicity of universes nested within our universe. Mass ejection from a cosmic quantum envelope is the cosmic equivalence of radioactivity, it signals ageing and eventual disappearance of the host periodic envelope from visibility. Reality is an imperturbable (ideal) Steady-State, observations thought to invalidate this view are hugely misinterpreted, an explosion in or of spacetime marking the beginning of time could not conceivably sustain, over the aeons, an accelerating expansion of metric space; furthermore, the cosmic microwave background is the zero-point energy or vacuum radiation. The active galactic nucleus or black hole is not a singularity, it is a two-way valve that facilitates circulation of mass-energy matrices across the four phases or ref. frames of reality. There is no new creation of space or matter, only continuous recycling in line with NASA’s recent observation.

Periodic orbits for a generalized Hénon-Heiles Hamiltonian system with an additional singular gravitational term

We study the periodic dynamics of the Hénon-Heiles Hamiltonian system with the additional singular gravitational term . The Hénon-Heiles modelizes how stars move around a galactic center. The addition of this singular gravitational term allows to modelize the motion of the stars in a pseudo or post-Newtonian dynamics. Thus this model allows to predict phenomena which cannot be detected by the classical Newtonian mechanics. Using the averaging theory of first order we study analytically the existence of two families of periodic orbits of this generalized Hénon-Heiles Hamiltonian system. Moreover we characterize when this generalized Hénon-Heiles Hamiltonian system has or has not a second C 1 first integral independent of the Hamiltonian.

Point-Mass Biomechanical Model of the Upper Extremity During Lofstrand Crutch-Assisted Gait.

We propose a point-mass biomechanical model to estimate the forces and moments supported by the upper extremity during Lofstrand crutch-assisted gait. This model is based on the Newtonian classical mechanics and the angular momentum theorem. The system arm-crutch is divided into three segments: 1) crutch, 2) wrist-elbow, and 3) elbow-shoulder. The theoretical model was experimentally validated with a disabled person with spinal cord injury. Two crutch-assisted gait patterns have been chosen to carry out the experimental validation: two-point reciprocal gait and swing-through gait. Six position markers (three placed on the arm and three placed on the crutch) and two force sensors (placed on the crutch) were used in experiments for testing the model. The results were compared with a distributed-mass model based on studies previously published, concluding that the relative mean difference between models is less than 3% Body Weight and 1% Body Weight times Height when forces and moments are estimated, respectively. Some advantages of using a point-mass model are summarized: simple formulation, easy to understand; require less numerical calculation reducing the computational cost; requires less position markers placed on the subject, increasing therefore the comfort of the subject.

Free variable mass nonlocal systems, jerks, and snaps, and their implications in rotating fluids in rockets

Dynamical systems with position varying mass are archetypal examples of classical mechanical systems with rocket engine being a typical realistic model. In the present study, we extend the classical Newtonian mechanics by replacing the kinetic energy by a nonlocal-in-time kinetic energy and the standard velocity by a fractional velocity. These replacements lead to an extension of Newton’s second law of motion which has interesting implications in incompressible fluid dynamics. As an application, we discuss the rotating fluid problem subject to a position varying fluid mass which occurs in rocket dynamics. Several features were observed, mainly the transition from order to disorder in rotating fluids in rockets.

Modelling of magnetic bead transport in a microvascular network

In in vivo applications of magnetic particles one crucial aspect is the control of their transport in the tissue microvasculature and their release to target areas. These mechanisms can be driven and influenced by external magnetic fields with large gradients. Experimental results can be elucidated with the aid of in silico models that can also be employed to design optimized multifunctional particles and magnetic field sources. In this framework, we have developed a numerical model that enables us to calculate the trajectory of an ensemble of magnetic nano/microbeads injected in a blood vessel and manipulated by an applied magnetic field. The model combines Navier-Stokes equations for the fluid dynamics simulation of blood flow with classical Newtonian mechanics for bead motion, performing the analysis in a 3D vessel segment reconstructed from a computed tomography scan. The numerical model is applied to study the influence of bead properties (size and magnetic moment) on both transport and adhesion rate, taking into account the interplay of magnetic and viscous drag forces, as well as magnetic dipole–dipole and steric interactions. We also consider different configurations of the external magnetic field source, in order to optimize bead accumulation and adhesion to the vessel wall in a specific target region, processes that can be driven by magnetic forces.

Generalized Newtonian fractional model for the vertical motion of a particle

Based on the Riemann-Liouville (R-L) fractional derivative and the generalized Newtonian law of gravitation, the nonlinear fractional differential equation describing the vertical motion of a particle is solved. Such solution is investigated to obtain the escape velocity (EV) following the fractional Newtonian mechanics. It is well known that the EV from the Earth’s gravitational field is about 11.18 km/s within the paradigm of the classical Newtonian mechanics using integer derivatives, but its value has not been yet determined in the scope of fractional calculus. Therefore, we can pose the question: Is the classical value of the EV identical when analyzed under the light of the fractional mechanics? The paper answers this question for the first time. It is found that the fractional escape velocity (FEV) depends on the non-integer order α and a parameter σ with dimension of seconds. The general relation between σ and α is established. The results reveal that the values of the FEV approaches the classical one when α → 1 and σ ≈ 5 × 103 seconds.

The English Galileo and His Vision of Projectile Motion under Air Resistance

This article presents a detailed discussion of the shape of the trajectory traced by a projectile under the forces of gravity and air resistance. In particular, our results confirm the insight of the English scientist Thomas Harriot into the motion of a projectile before the development of Newtonian classical mechanics. Our approach is based on the fact that the flight path of a resisted projectile is implemented by a strictly concave function for which the derivative is also strictly concave.

Relational Density Theory: Nonlinearity of Equivalence Relating Examined through Higher-Order Volumetric-Mass-Density.

We propose relational density theory, as an integration of stimulus equivalence and behavioral momentum theory, to predict the nonlinearity of equivalence responding of verbal humans. Consistent with Newtonian classical mechanics, the theory posits that equivalence networks will demonstrate the higher order properties of density, volume, and mass. That is, networks containing more relations (volume) that are stronger (density) will be more resistant to change (i.e., contain greater mass; mass = volume * density). Data from several equivalence experiments that are not easily interpreted through existing accounts are described in terms of the theory, generating predictable results in most cases. In addition, we put forward the higher-order properties of relational acceleration and gravity, which follow directly from the theory and may inspire future researchers to evaluate the seemingly self-organizing nature of human cognition. Finally, we conclude by describing avenues for real-world translation, considering past research interpreted through relational density theory, and call for basic experimental research to validate and extend core theoretical assumptions.

The Falling Body Problem in Quantum Calculus

The quantum calculus, $q$-calculus, is a relatively new branch in which the derivative of a real function can be calculated without limits. In this paper, the falling body problem in a resisting medium is revisited in view of the $q$-calculus to the first time. The $q$-differential equations describing the vertical velocity and distance of the body are obtained. Accordingly, exact expressions for the vertical velocity and the vertical distance are provided. The solutions are expressed in terms of the small $q$-exponential function which is an elementary function in the $q$-calculus. The dimensionality of the obtained formulae of the velocity and the distance are also analyzed. In addition, the present exact solutions reduce to the corresponding solutions in classical Newtonian mechanics when the quantum parameter $q$ tends to one.

Analysis of influencing factors on fusion accuracy of virtual gyroscope technology and new data fusion method

In view that the MEMS gyroscope has low precision, the virtual gyro is used to improve the output precision of the MEMS gyro. By analyzing the factors affecting the fusion precision of virtual gyro, the essential relationship between gyro noise correlation and the fusion precision is obtained. In static, the influence of the noise characteristics and noise correlation coefficient on the output precision of MEMS gyro array is great; while in dynamic, the influence of the noise characteristics is small due to system modeling error and non-linear error, the influence of the angular rate modeling accuracy is great. Therefore, the Taylor model is used to extend the motion model described by classical Newtonian mechanics, and the angular motion model of different modeling series is established. This paper introduces the improved current statistical model, uses the modified Rayleigh function to describe the angular motion variable, establishes the zero-mean colored driving noise model, realizes the adaptive adjustment of the frequency and the driving noise intensity, and establishes the high-precision dynamic angular rate model of different modeling series. Finally, the improved interactive multi-model Kalman filter is used to fuse the output of the gyro in the MEMS gyro array. The simulation results show that the proposed method can improve the output precision of MEMS gyroscopes effectively and has certain engineering application value.

The choice of dynamic variables in quantum theory

The influence of various choices of dynamic variables in quantum theory on the interpretation of measurement results and experiments are discussed. Dynamic variables in the generally accepted quantum mechanics have no visual sense, which in turn leads to the loss of the image of the studied phenomena and processes of the microworld. Thus, quantum mechanics forces us to abandon the possibility of even mentally imagining the conditions that determine the behavior of an individual system in a quantum region. Also, various representations of the wave function and their use in solving dynamic equations are shown. By now, quantum mechanics is not a complete theory. It resembles classical (Newtonian) mechanics, which explains how movement occurs as a result of the action of certain forces, but does not say what kind of forces it is. Thus, before the advent of basic theories, the application of quantum mechanics to specific physical problems always implied the need to build certain guesses about the nature of these forces.

Stability analysis of a class of non-newtonian fluids based on generalized vector variational-like inequalities on riemannian manifold

Fluid mechanics is a branch of mechanics. It is the science of studying fluid phenomena and related mechanical behaviors. So far, the mutual soaking and fusion between fluid mechanics and other disciplines have formed many branches, many physicists and Mathematicians are working on this aspect of research. The classical Newtonian fluid mechanics believe that in parallel flow, the shear force is proportional to the shear rate, and the proportional coefficient is called the viscosity coefficient. In recent years, with the increasing importance of non-Newtonian fluids, people have found that research on non-Newtonian flow is necessary. The variational inequalities based on Riemannian manifolds were first proposed by S.Z.Németh. S.Z.Németh studied the existence of solutions to variational inequalities on Hadamard manifolds. For the equivalence of non-differentiable vector optimization problems on Riemannian manifolds and generalized weak vector variational-like inequalities, we give some new conclusions.

On the existence of exotic matter in classical Newtonian mechanics

According to Newton’s law of gravitation, the force between two particles depends upon their inertial, as well as their active and passive gravitational masses. For ordinary matter, all three of these are equal and positive. We consider here the more general case where these quantities are equal in magnitude for a given particle but can differ in sign. The resulting set of possible interactions allows each particle type to be assigned to one of precisely four different classes, and the results of N-body simulations show that the corresponding dynamics can give rise to a fairly rich spectrum of possible outcomes, some of which are familiar from nature at various scales. Total energy and momentum are conserved by all of these interactions if the definitions of momentum and kinetic and potential energy are suitably generalized.

The Classification of Mechanical Models of Road Pavements

AbstractA review of mechanical models of road pavements in the form of a proposal of classification of these models is presented. It is assumed an autonomy of the following elements of pavement model: the models of structural layers, the subgrade model, the interlayer bonding models, including bonding of pavement structure with its subgrade, the models of external impacts on pavement layers, including load of heavy traffic, the models of pavement environment impacts on structural layers’ borders (lateral) and subgrade borders (including the lower one) – according to the selected criteria such as structural criterion, material criterion (physical criterion), dimension criterion and model scope (purpose) criterion − in the frame of assumptions of the classical Newtonian deterministic mechanics. The presented attempt to classify mechanical models of road pavements supports to orientate the roadmen community within a scope of the mechanistic modelling of these structures.

The choreography of life

Part of our work as biochemists is to describe the choreography of life at the molecular scale. This sounds complicated, and it is, not least because we have to apply different approaches across the scale of study that could be considered ‘molecular’. At the most finite end of the spectrum, i.e., atoms and small molecules, researchers need to invoke quantum mechanics to describe behaviour. As we move up to larger complexes, however, we transition to a different subset of physics, where we can begin to describe movement via the more familiar and approachable set of rules found in classical Newtonian mechanics. This is the kind of physics we encounter in our everyday lives and which describes the actions of industrial machinery. And it is in this kind of language that we tend to understand the movement of molecular machines, such as the archetypal ATP synthase complex.

Nonlocal-in-time kinetic energy in nonconservative fractional systems, disordered dynamics, jerk and snap and oscillatory motions in the rotating fluid tube

In this article we generalize the basic theoretical properties of nonlocal-in-time kinetic energy approach introduced in the framework of nonlocal classical Newtonian mechanics for the case of fractional dynamical systems explored in the context of the fractional actionlike variational approach. Two independent fractionally Lagrangians weights are considered independently: the Riemann-Liouville fractional weight and the extended exponentially fractional weight. For each weight, the corresponding nonlocal fractional Newton's law of motion is derived. Three main physical applications were discussed in details: free particles, oscillators and dynamics of particles in a rotating tube with earth frame. A number of differential equations depending on fractional and nonlocal-in-time parameters were obtained and their solutions are discussed accordingly. For specific parameters and particular initial conditions, it was observed that the dynamics exhibit a kind of strange phase plot trajectories that indicate the presence of disordered motions. However one of the main results concerns the physics of particles in the rotating tube which display, for specific values of fractional and nonlocal-in-time parameters, oscillatory motions controlled by the nonlocal-in-time parameter.

Why do we live in a quantum world?

Anybody who has ever studied quantum mechanics knows that it is a very counterintuitive theory, even though it has been an incredibly successful theory. This paper aims to remove this counterintuitiveness by showing that the laws of quantum mechanics are a natural consequence of classical Newtonian mechanics combined with the digital universe hypothesis of Konrad Zuse and Edward Fredkin. We also present a possible way to test the digital universe hypothesis.

On the Classical Schrödinger Equation

In this paper, the classical Schrödinger equation (CSE), which allows the study of classical dynamics in terms of wave functions, is analyzed theoretically and numerically. First, departing from classical (Newtonian) mechanics, and assuming an additional single-valued condition for the Hamilton’s principal function, the CSE is obtained. This additional assumption implies inherent non-classical features on the description of the dynamics obtained from the CSE: the trajectories do not cross in the configuration space. Second, departing from Bohmian mechanics and invoking the quantum-to-classical transition, the CSE is obtained in a natural way for the center of mass of a quantum system with a large number of identical particles. This quantum development imposes the condition of dealing with a narrow wave packet, which implicitly avoids the non-classical features mentioned above. We illustrate all the above points with numerical simulations of the classical and quantum Schrödinger equations for different systems.