Related papers: The Two Rigid Body Interaction using Angular Momen…
Evaluating multi-center molecular integrals with Cartesian Gaussian-type basis sets has been a long-standing bottleneck in electronic structure theory calculation for solids and molecules. We have developed a vector-coupling and…
A two-dimensional body, exhibiting a slight rotational movement, moves in a rarefied medium of particles which collide with it in a perfectly elastic way. In previously realized investigations by the first two authors, Plakhov & Gouveia…
An efficient and accurate computational approach is proposed for optimal attitude control of a rigid body. The problem is formulated directly as a discrete time optimization problem using a Lie group variational integrator. Discrete…
Being able to reproduce physical phenomena ranging from light interaction to contact mechanics, simulators are becoming increasingly useful in more and more application domains where real-world interaction or labeled data are difficult to…
This work introduces a port-Hamiltonian (PH) model for constrained mechanical systems, which is directly derived from the Lagrangian equations of motion. The present PH framework incorporates a singularity-free director representation of…
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of…
Many-body forces are sometimes a relevant ingredient in various fields, such as atomic, nuclear or hadronic physics. Their precise structure is generally difficult to uncover. So, phenomenological effective forces are often used in…
We outline a new method suggested by Conway (2016) for solving the two-body problem for solid bodies of spheroidal or ellipsoidal shape. The method is based on integrating the gravitational potential of one body over the surface of the…
Angular momentum is important concept in physics, and its phase space properties are important in various applications. In this work phase space analysis of the angular momentum is made from its classical definition, and by imposing…
While studying the motion of a heavy symmetric top, in general, constants of motion are used. Some students may want to understand the motion in terms of torque, which can lie on their routine based on the usage of Newton's second law.…
Constrained mechanical multibody systems arise in many important applications like robotics, vehicle and machinery dynamics and biomechanics of locomotion of humans. These systems are described by the Euler-Lagrange equations which are…
Recently, the centroidal momentum dynamics has received substantial attention to plan dynamically consistent motions for robots with arms and legs in multi-contact scenarios. However, it is also non convex which renders any optimization…
Robotic manipulation in unstructured environments requires planners to reason jointly about free-space motion and sustained, frictional contact with the environment. Existing (local) planning and simulation frameworks typically separate…
The two-body problem with a central interaction on simply connected constant curvature spaces of an arbitrary dimension is considered. The explicit expression for the quantum two-body Hamiltonian via a radial differential operator and…
We present a fast and feature-complete differentiable physics engine, Nimble (nimblephysics.org), that supports Lagrangian dynamics and hard contact constraints for articulated rigid body simulation. Our differentiable physics engine offers…
We present a simple model for the friction of two solid bodies moving against each other. In a self consistent way we can obtain the dependence of the macroscopic friction force as a function of the driving velocity, the normal force and…
This paper presents the analytic modeling of mobile heavy-duty manipulators with actively articulated suspension and its optimal control to maximize its static and dynamic stabilization. By adopting the screw theory formalism, we consider…
This letter studies a distributed collision avoidance control problem for a group of rigid bodies on a sphere. A rigid body network, consisting of multiple rigid bodies constrained to a spherical surface and an interconnection topology, is…
This paper presents thorough mathematical modeling, control law development, and simulation of virtual structure formations which are inspired by the characteristics of rigid bodies. The stable constraint forces that establish the rigidity…
This paper proposes a unified approach for dynamic modeling and simulations of general tensegrity structures with rigid bars and rigid bodies of arbitrary shapes. The natural coordinates are adopted as a non-minimal description in terms of…