Related papers: Dynamic Modeling and Simulation of a Rotational In…
In molecular dynamics, penalized overdamped Langevin dynamics are used to model the motion of a set of particles that follow constraints up to a parameter $\varepsilon$. The most used schemes for simulating these dynamics are the Euler…
In the course of basic physics, more precisely the course of classical mechanics should be understood as clearly as possible the subject of rotational dynamics for students of science and engineering, to have clarity with the issues…
We discuss several steady-state rotation and oscillation modes of the planar parametric rotator and pendulum with damping. We consider a general elliptic trajectory of the suspension point for both rotator and pendulum, for the latter at an…
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…
The derivation of a linear fractional representation (LFR) model for a flexible, spinning and uniform Euler-Bernoulli beam is accomplished using the {Lagrange} technique, fully capturing the centrifugal force generated by the spinning…
Locomotion of legged machines faces the problems of model complexity and computational costs. Algorithms based on complex models and/or reinforcement learning exist to solve the walking control task. In this project, we aim to develop a…
The author considers the planar rotational motion of the mathematical pendulum with its pivot oscillating both vertically and horizontally, so the trajectory of the pivot is an ellipse close to a circle. The analysis is based on the exact…
A new algorithm is introduced to integrate the equations of rotational motion. The algorithm is derived within a leapfrog framework and the quantities involved into the integration are mid-step angular momenta and on-step orientational…
This work presents a numerical analysis of computing transition states of semilinear elliptic partial differential equations (PDEs) via the index-1 saddle dynamics, or equivalently, the gentlest ascent dynamics. To establish clear…
Reconfigurable robots are at the forefront of robotics innovation due to their unmatched versatility and adaptability in addressing various tasks through collaborative operations. This paper explores the design and implementation of a novel…
We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…
Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…
We identify the nonlinear normal modes spawning from the stable equilibrium of a double pendulum under gravity, and we establish their connection to homoclinic orbits through the unstable upright position as energy increases. This result is…
In this technical note, we consider a dynamic linear, cantilevered rectangular plate. The evolutionary PDE model is given by the fourth order plate dynamics (via the spatial biharmonic operator) with clamped-free-free-free boundary…
If one wants to explore the properties of a dynamical system systematically one has to be able to track equilibria and periodic orbits regardless of their stability. If the dynamical system is a controllable experiment then one approach is…
A finite element based computational scheme is developed and employed to assess a duality based variational approach to the solution of the linear heat and transport PDE in one space dimension and time, and the nonlinear system of ODEs of…
We present analytical and numerical results on integrability and transition to chaotic motion for a generalized Ziegler pendulum, a double pendulum subject to an angular elastic potential and a follower force. Several variants of the…
This article presents the real-time implementation of the model predictive control for tracking formulation to control a two-wheeled inverted pendulum robot. This formulation offers several advantages over standard MPC formulations at the…
In recent years, aerial platforms have evolved from passive flying sensors into versatile, contact-aware robotic systems, leading to rapid advances in platform design. Standard coplanar and collinear quadrotors have been complemented by…
Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is…