Rigid Body Dynamics Research Articles

Experimental and numerical investigation on the unsteady interaction in longitudinal stage separation for parallel-staged two-body configuration

Hypersonic stage separation is a significant process, probably involving complex aerodynamic interaction, which determines the survival of two-stage-to-orbit (TSTO) vehicles. The longitudinal stage separation (LSS) scheme is proposed to improve the safety of the parallel-staged TSTO vehicle, where a small interstage gap may result in weak interference. Therefore, an experimental and numerical study of LSS for the parallel-staged TSTO vehicle at Mach 7 with different angles of attack (AoA) is carried out. The dynamic interaction, including variations in the shock structure, wall pressure distribution, and unsteady aerodynamics, is investigated by testing and numerical simulation. The LSS experiments for the TSTO vehicle were performed using a high-speed pneumatic ejection launch system in the JF-12 shock tunnel, and the method was developed using high-speed visualization and image processing techniques to capture the separating trajectory. The numerical simulations were carried out using the overset grid method and solving the Navier–Stokes equations coupled with the rigid body dynamics equations to obtain the laminar flows over the TSTO vehicle during LSS. The qualitative and quantitative comparison of the test and numerical results showed good agreement in terms of aerodynamic performance, flowfield pattern, wall pressure, and separation trajectory. They show that the small interstage gap of the LSS leads to weak type I and VI shock–shock interactions, with short-duration weak shock reflection at a higher AoA. Furthermore, no shock reflection or interstage gap is observed at lower AoA. Moreover, no stage recontact is observed, and the safety and feasibility of LSS for parallel-staged TSTO vehicles are demonstrated.

The Ricci decomposition of the inertia tensor for a rigid body in arbitrary spatial dimensions

The rotations of rigid bodies in Euclidean space are characterized by their instantaneous angular velocity and angular momentum. In an arbitrary number of spatial dimensions, these quantities are represented by bivectors (antisymmetric rank-2 tensors), and they are related by a rank-4 inertia tensor. Remarkably, this inertia tensor belongs to a well-studied class of algebraic curvature tensors that have the same index symmetries as the Riemann curvature tensor field used in general relativity. Any algebraic curvature tensor can be decomposed into irreducible representations of the orthogonal group via the Ricci decomposition. We calculate the Ricci decomposition of the inertia tensor for a rigid body in any number of dimensions, and we find that (unlike for the Riemann curvature tensor field) its traceless Weyl tensor is always zero, so the inertia tensor is completely characterized by its (rank-2) Ricci contraction. So unlike in general relativity, the traceless Weyl tensor does not cause any qualitatively new phenomenology for rigid-body dynamics in n≥4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n \\ge 4$$\\end{document} dimensions.

An expansion method for generating travelling wave solutions for the (2 + 1)-dimensional Bogoyavlensky-Konopelchenko equation with variable coefficients

This paper presents a new approach to studying nonlinear evolution equations with variable coefficients and applies it to the Bogoyavlensky-Konopelchenko equation. The Bogoyavlensky-Konopelchenko equation, which describes the interaction between a long wave and a Riemann wave in a special fluid, has many applications in fluid dynamics of mathematical physics. Most studies in the literature focus on the Bogoyavlensky-Konopelchenko equation with constant coefficients. This can lead to deficiencies in the understanding of the physical phenomena revealed by the model. To overcome this limitation, terms with time-varying coefficients are introduced into the Bogoyavlensky-Konopelchenko equation. With the addition of these terms, the model is brought closer to the real problem and the physical phenomenon can discussed with more freedom. This study has three main focal points. Firstly, it introduces a novel approach designed for nonlinear evolution equations characterized by variable coefficients. Secondly, the proposed method is applied to generate solutions for the Bogoyavlensky-Konopelchenko equation, showcasing distinctions from existing literature. Finally, the effects of time-varying coefficients on solitons and their interactions with each other in the generated travelling wave solutions are analysed in detail under certain restrictive conditions. The results shed light on the physical behavior of the Bogoyavlensky-Konopelchenko equation with variable coefficients and contribute to a better understanding of similar models. The proposed method opens new possibilities for the study of nonlinear evolution equations with variable coefficients and provides avenues for analytical investigation of their solutions.

Evidence for Electron Precipitation Diffused by Rising‐Tone Quasiperiodic Whistler Waves in Extremely Low L−Shells Observed by CSES

AbstractBased on the observations by the sun‐synchronous circular orbit China Seismo‐Electromagnetic Satellite(CSES), a typical case of the rising‐tone quasiperiodic (QP) emissions with a large period of around 2 min was reported to appear on the dayside on 23 October 2021. The frequency of QP waves ranges from 2,000 ∼ 3,000 Hz and the wave spectral structure consists of four elements with right‐handed polarization. Three elements of them are located at extremely low L‐shells from 2 ∼ 3.5. The periodic precipitating fluxes of 100 ∼ 400 keV electrons were found in the conjugate region also observed by CSES, which appeared in the same magnetic field lines with the elements of QP waves, respectively. By numerical simulations of quasi‐linear diffusion theory, we confirm that QP emissions can effectively precipitate energetic electrons near the loss cone into the atmosphere in the inner radiation belt. To our best knowledge, this is the first evidence that the rising‐tone QP whistler waves scatter electrons in the inner radiation belt. This new finding will help to deepen our understanding of the electron precipitation dynamics in radiation belt physics.

Soliton solutions to a wave equation using the (ϕ'/ϕ)– expansion method

This article aims to explore and examine general soliton solutions within the context of the generalized Benjamin-Bona-Mahony equation. This equation is a significant mathematical tool employed in the study of wave dynamics in ocean physics. In this paper, we investigate and generate new propagating soliton solutions for the above-mentioned equation using the (ϕ′/ϕ) − expansion method, an elegant mathematical approach. Rational, trigonometric, and hyperbolic functions are used to express these solutions. In order to provide a visual comprehension of the complex physical phenomena regulating the system, we additionally demonstrate graphics in two and three dimensions. The study explores a range of parameter configurations that yield distinct soliton solutions. By visually depicting these solutions based on specific parameter choices, a deeper comprehension of the system's complex behavior is achieved. The article sheds light on novel findings concerning soliton solutions for the mentioned equation, unveiling previously unnoticed aspects of this captivating mathematical problem.

Robust control of gust-induced vibration of highly flexible aircraft

This paper mainly addresses the gust suppression and alleviation of highly flexible aircraft using the model predictive controller (MPC) based on linear parameter-varying (LPV) models. The dynamic behavior of highly flexible aircraft is modeled by a coupled nonlinear aeroelastic and flight dynamic formulation. Conventional trailing-edge flaps along the main wings and tails are deployed to provide the required loads for the wing vibration control and/or longitudinal flight attitude control of the slender vehicle. The coupled dynamic equations are performed with linearization and model reduction about a series of nonlinear equilibria to derive reduced-order LPV models. This work considers two quantities as the scheduling parameters in building the LPV models: the gust-induced angle of attack and the modal magnitude of wing deformation. With the reduced-order LPV model, MPC is designed to minimize the wing vibration and rigid-body motions excited by the time-domain Dryden gust perturbation. The proposed LPV modeling is capable of describing large wing deformations, and the LPV-MPC innovatively previews the scheduling parameter and gust disturbance in the prediction horizon. The closed-loop flight responses of a highly flexible aircraft with gust disturbance are presented in the numerical studies, which demonstrate the effectiveness of controlling coupled vibrations and rigid-body dynamics of such slender vehicles.

A study of a nonlinear vibration isolator supported on an imperfect boundary plate

The research on the nonlinear vibration isolation of continuum systems always focuses on the perfect boundary conditions. In this work, nonlinear isolation of transverse vibrations of the arbitrary boundary rectangular plate was investigated. A novel analytical approach was proposed. The rigid body dynamics and high-order energy Fourier series expansion method were utilized to establish a mathematical model of the arbitrary boundary nonlinear continuum system. This method involves the simultaneous Fourier series expansion in temporal and spatial domains. The dynamic behaviors of an arbitrary boundary rectangular plate with nonlinear vibration isolators can be described through a harmonic balance analysis together with arc-length continuation. The convergence and stability for the frequency response functions were checked via the Lyapunov stability theory. The numerical results supported the analytical solutions. Both the analytical and numerical results demonstrated that nonlinear broadband vibration isolation is sensitive to the elasticity of the arbitrary boundary flexible foundation. Furthermore, increasing damping can effectively suppress the transmission of low-order vibrations and control the divergence of higher-order vibrations. Finally, an experiment rig was designed to validate the nonlinear isolation of the transverse vibrations of an arbitrary boundary plate.

Impact forces in backward falls: Subject-specific video-based rigid body simulation of backward falls.

A critical missing component in the study of real-world falls is the ability to accurately determine impact forces resulting from the fall. Subject-specific rigid body dynamic (RBD) models calibrated to video captured falls can quantify impact forces and provide additional insights into injury risk factors. RBD models were developed based on five backward falls captured on surveillance video in long-term care facilities in British Columbia, Canada. Model joint stiffness and initial velocities were calibrated to match the kinematics of the fall and contact forces were calculated. The effect of joint stiffnesses (neck, lumbar spine, hip, and knee joint) on head contact forces were determined by modifying the calibrated stiffness values ±25%. Fall duration, fall trajectories, and maximum velocities showed a close match between fall events and simulations. The maximum value of pelvic velocity difference between Kinovea (an open-source software 2D digitization software) and Madymo multibody modeling was found to be 6% ± 21.58%. Our results demonstrate that neck and hip stiffness values have a non-significant yet large effect on head contact force (t(3) = 1, p = 0.387 and t(3) = 2, p = 0.138), while lower effects were observed for knee stiffness, and the effect of lumbar spine stiffness was negligible. The subject-specific fall simulations constructed from real world video captured falls allow for direct quantification of force outcomes of falls and may have applications in improving the assessment of fall-induced injury risks and injury prevention methods.

Space-time rigid multibody dynamics

In this contribution, we apply space-time formulation on constrained rigid body dynamics. In particular, we discretize directly Hamilton’s principle using appropriate space-time approximation spaces for the variational problem. Moreover, we make use of a rotationless formulation for the rigid bodies, and thus we have to define appropriate approximation spaces for the Lagrange multipliers as well. Moreover, we make use of Livens’ principle, introducing independent quantities for the position, velocity, and momentum, where the latter can be considered as Lagrange multipliers, and we apply this concept to the space-time rigid body formulation. Finally, we demonstrate the convergence of the different approaches and the superiority in terms of computational effort, and thus total energy consumption of dynamical simulations.

Combining experiments, theory, and computer simulation: Application of dynamics analysis of unbalanced wheels rolling without sliding on horizontal paths

AbstractRigid solid body dynamics is a key element of the undergraduate mechanical engineering curriculum. In a context of reverse engineering and/or sustainable development, being able to analyze the mechanical and material properties of a system without damaging it is a required skill. In this work, two systems based on wheels rolling over horizontal paths without sliding are studied: an unbalanced hollow cylinder and a wheel with displaced mass assembly. Four generations of last year's bachelor's students in mechanical engineering, representing a hundred people a year, followed a total of 12 h of practical sessions working on such systems. Without focusing on the programming part, this paper aims at showing how computer tools can help and improve a rigid solid body dynamics course. The objectives were to develop, apply, and analyze this teaching sequence, allowing students to (i) perform and characterize experimental measurements, (ii) establish systems motion equations, and (iii) think about dynamics results through cross‐talks between different techniques such as geometrical and analytical methods as well as computer‐assisted design tools. Different analysis methods of these systems could be discussed in the context of the classes, successfully bringing pertinent reflections to the students. The possibility of transferring such discussions to other contexts proved to be wide, thanks to computer science, dynamics software, other analysis methods and applications.

Differentiable hybrid neural modeling for fluid-structure interaction

Solving complex fluid-structure interaction (FSI) problems, which are described by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics based solvers are inadequate to handle the increasing demand for large-scale and long-period simulations. The ever-increasing availability of data and rapid advancement in deep learning (DL) have opened new avenues to tackle these challenges through data-enabled modeling. The seamless integration of DL and classic numerical techniques through the differentiable programming framework can significantly improve data-driven modeling performance. In this study, we propose a differentiable hybrid neural modeling framework for efficient simulation of FSI problems, where the numerically discretized FSI physics based on the immersed boundary method is seamlessly integrated with sequential neural networks using differentiable programming. All modules are programmed in JAX, where automatic differentiation enables gradient back-propagation over the entire model rollout trajectory, allowing the hybrid neural FSI model to be trained as a whole in an end-to-end, sequence-to-sequence manner. Through several FSI benchmark cases, we demonstrate the merit and capability of the proposed method in modeling FSI dynamics for both rigid and flexible bodies. The proposed model has also demonstrated its superiority over baseline purely data-driven neural models, weakly-coupled hybrid neural models, and purely numerical FSI solvers in terms of accuracy, robustness, and generalizability.

The Design of a Tracking Controller for Flexible Ball Screw Feed System Based on Integral Sliding Mode Control with a Generalized Extended State Observer

This article proposes a servo control strategy for compensating matched and mismatched perturbations in flexible ball screw feed systems to improve their tracking performance. The perturbations that satisfy or dissatisfy the matching conditions include external disturbances, parameter uncertainties, and unmodeled dynamics. The flexible ball screw feed model includes both a rigid body and first-order axial structural dynamics. A generalized extended state observer is adopted to observe the matched and mismatched perturbations and various state variables of the system, and an improved integral sliding mode controller is proposed that can simultaneously compensate for the perturbations of the system that satisfy and dissatisfy the matching conditions. In addition, vibration compensation is designed for first-order axial vibration of the system to develop a controller that can quickly and accurately track the ideal reference trajectory, suppress system structural vibrations, and be robust to time-varying uncertainties and external disturbances. Finally, the tracking performance, anti-interference performance, and vibration suppression performance of the designed controller are verified via simulation and comparative experiments.

High-order harmonic interferometry for the study of intensity-dependent dipole phase

Abstract High-order harmonics are ideal probes to resolve the attosecond dynamics of strong field recollision process. In this work, an easy-to-implement phase mask is utilized to covert the Gaussian beam to TEM01 transverse electromagnetic mode, allowing the realization of two source interferometry of high-order harmonics. We experimentally measured the intensity-dependence of dipole phase directly with high-order harmonic interferometry, in which the driving laser intensity can be precisely adjusted. The classical electron excursion simulations reproduce the experimental findings quite well, demonstrating that Coulomb potential plays subtle roles on the movement of electrons for harmonics near the ionization threshold. This work is of great importance for precision measurements of ultrafast dynamics in strong-field physics.

Aeroelasticity Model for Highly Flexible Aircraft Based on the Vortex Lattice Method

With the increasing use of composite materials in aviation, structural aircraft design often becomes limited by stiffness, rather than strength. As a consequence, aeroelastic analysis becomes more important to optimize both aircraft structures and control algorithms. A low computational cost aeroelasticity model based on VLM and rigid-body dynamics is proposed in this work. UAV flight testing is performed to evaluate the accuracy of the proposed model. Two flight sections are chosen to be modeled based on recorded aerodynamic surface control data. The calculated accelerations are compared with recorded flight data. It is found that the proposed model adequately captures the general flight profile, with acceleration peak errors between −6.2% and +8.4%. The average relative error during the entire flight section is 39% to 44%, mainly caused by rebounds during the beginning and end of pull-up maneuvers. The model could provide useful results for the initial phases of aircraft control law design when comparing different control algorithms.

Heteroclinic chaos detecting in dissipative mechanical systems: Chaotic regimes of compound nanosatellites dynamics

The problem of heteroclinic chaos detecting is considered with the help of the Melnikov method. This paper presents the Melnikov method adaptation based on investigation of a nanosatellite attitude dynamics in the presence of internal dissipation properties. The need for this adaptation is determined by dynamical aspects of perturbing oscillations acting with damping amplitudes. In this case formal analytical exponential growth of perturbations values in reverse time takes place while the classical Melnikov integral does not converge.The adaptation of the Melnikov method allows investigating the heteroclinic chaos in mechanical systems with internal dissipation properties. As a prime example of this adaptation, the research presents the complete study of chaotic attitude dynamics of a nanosatellite with a slightly movable unit under action of its damped oscillations considered as perturbations. Moreover, the considered research of the nanosatellite attitude dynamics discovers a range of important tasks in the area of a rigid body dynamics under different perturbations with damping.

Hamiltonian Neural Network 6-DoF Rigid-Body Dynamic Modeling Based on Energy Variation Estimation

This study introduces a novel deep modeling approach that utilizes Hamiltonian neural networks to address the challenges of modeling the six degrees of freedom rigid-body dynamics induced by control inputs in various domains such as aerospace, robotics, and automotive engineering. The proposed method is based on the principles of Hamiltonian dynamics and employs an inductive bias in the form of a constructed bias for both conservative and varying energies, effectively tackling the modeling issues arising from time-varying energy in controlled rigid-body dynamics. This constructed bias captures the information regarding the changes in the rigid body’s energy. The presented method not only achieves highly accurate modeling but also preserves the inherent bidirectional time-sliding inference in Hamiltonian-based modeling approaches. Experimental results demonstrate that our method outperforms existing techniques in the time-varying six degrees of freedom dynamic modeling of aircraft and missile guidance, enabling high-precision modeling and feedback correction. The findings of our research hold significant potential for the kinematic modeling of time-varying energy systems, parallel system state prediction and control, inverse motion inference, and autonomous decision-making in military applications.

Incorporation of Rigid Body Dynamics into Indirect Hypersonic Trajectory Optimization

This investigation demonstrates hypersonic trajectory optimization using planar rigid body dynamics within the indirect trajectory optimization framework. Employing rigid body dynamics captures the coupling between the optimal trajectory, the vehicle geometry, mass distribution, and control configuration. This provides trajectories that implicitly account for the maneuverability of the vehicle, wherein the vehicle is guaranteed to follow the angle-of-attack profile. This is unlike point-mass dynamics, wherein the angle-of-attack or angle-of-attack rate is directly used as the control variable, and maneuverability must be accounted for using bounds on these quantities. This is not straightforward because these bounds are dependent on flight conditions and are not constant for the entire trajectory. As a result, point-mass dynamics can produce infeasible solutions if these bounds are not properly handled. When using rigid body dynamics, these bounds are a consequence of the flight dynamics and are not required to be explicitly enforced, thereby circumventing the challenge with dynamic bounds on angle-of-attack and angle-of-attack rate altogether. Additionally, optimal trajectories calculated using rigid body dynamics more accurately reflect the drag penalties incurred when maneuvering the vehicle, such as when deflecting the aerodynamic control surfaces. The incurred drag penalties become critical in high-performance applications, wherein the terminal velocity is required to be maximized. Also, because the trajectory is coupled to the vehicle geometry, mass distribution, and control architecture, the optimal trajectory can be concurrently analyzed with the vehicle configuration, thereby enabling multidisciplinary design analysis. Despite these benefits offered by employing rigid body dynamics in trajectory optimization, there is limited literature in this regard, and none of them explored in this investigation employs indirect methods. This investigation fills this gap in the indirect trajectory optimization arena.

Rigid-Body Dynamics from the Euler Equations to the Attitude Control of Spacecraft in the Works of Scientists from Saint Petersburg State University. Part 1

Rigid-Body Dynamics from the Euler Equations to the Attitude Control of Spacecraft in the Works of Scientists from Saint Petersburg State University. Part 1

Dynamic Rigid Bodies Mining and Motion Estimation Based on Monocular Camera.

Dynamic object perception is an important yet challenging direction in the field of robot navigation. Without any prior knowledge about motion and objects, a novel dynamic rigid bodies mining and motion estimation method based on monocular camera is proposed in this article. Different from the existing works based on sampling that associate feature points to motion hypotheses according to the reprojection errors, our work endeavors to find the intrinsic relevance among motion hypotheses. To represent this relevance, the concept of the probabilistic field on the Lie group Sim(3) manifold is introduced, which is established using random sampling. It provides a computable way for the regions on the manifold where rigid bodies possibly appear. The probability of a motion hypothesis falling on a region is expressed by its confidence. The regions with large confidences in the probabilistic field are selected as potential rigid bodies, whose corresponding feature points are further sampled for pose calculation. As a result, the randomness of sampling is reduced and the inliers for possible rigid bodies are enhanced, which guarantees the accuracy of motion estimation. On this basis, the tracking of rigid bodies is achieved. The proposed method distinguishes the feature points of dynamic objects with 3-D motion from those in the static background, thus enabling simultaneous localization and mapping (SLAM) to be initialized in dynamic environments. The experimental results on the KITTI, Hopkins 155, and MTPV62 datasets demonstrate the effectiveness. Comparison experiments indicate that our method outperforms the other methods in sensitivity of dynamic objects perception.

Learning Physically Realizable Skills for Online Packing of General 3D Shapes

We study the problem of learning online packing skills for irregular 3D shapes , which is arguably the most challenging setting of bin packing problems. The goal is to consecutively move a sequence of 3D objects with arbitrary shapes into a designated container with only partial observations of the object sequence. We take physical realizability into account, involving physics dynamics and constraints of a placement. The packing policy should understand the 3D geometry of the object to be packed and make effective decisions to accommodate it in the container in a physically realizable way. We propose a Reinforcement Learning (RL) pipeline to learn the policy. The complex irregular geometry and imperfect object placement together lead to huge solution space. Direct training in such space is prohibitively data intensive. We instead propose a theoretically provable method for candidate action generation to reduce the action space of RL and the learning burden. A parameterized policy is then learned to select the best placement from the candidates. Equipped with an efficient method of asynchronous RL acceleration and a data preparation process of simulation-ready training sequences, a mature packing policy can be trained in a physics-based environment within 48 hours. Through extensive evaluation on a variety of real-life shape datasets and comparisons with state-of-the-art baselines, we demonstrate that our method outperforms the best-performing baseline on all datasets by at least 12.8% in terms of packing utility. We also release our datasets and source code to support further research in this direction. 1