Equations of motion

About: Equations of motion is a research topic. Over the lifetime, 33294 publications have been published within this topic receiving 791282 citations. The topic is also known as: equation of motion.

Mathematical methods of classical mechanics

Abstract: Part 1 Newtonian mechanics: experimental facts investigation of the equations of motion. Part 2 Lagrangian mechanics: variational principles Lagrangian mechanics on manifolds oscillations rigid bodies. Part 3 Hamiltonian mechanics: differential forms symplectic manifolds canonical formalism introduction to pertubation theory.

Essential dynamics of proteins

Abstract: Analysis of extended molecular dynamics (MD) simulations of lysozyme in vacuo and in aqueous solution reveals that it is possible to separate the configurational space into two subspaces: (1) an "essential" subspace containing only a few degrees of freedom in which anharmonic motion occurs that comprises most of the positional fluctuations; and (2) the remaining space in which the motion has a narrow Gaussian distribution and which can be considered as "physically constrained." If overall translation and rotation are eliminated, the two spaces can be constructed by a simple linear transformation in Cartesian coordinate space, which remains valid over several hundred picoseconds. The transformation follows from the covariance matrix of the positional deviations. The essential degrees of freedom seem to describe motions which are relevant for the function of the protein, while the physically constrained subspace merely describes irrelevant local fluctuations. The near-constraint behavior of the latter subspace allows the separation of equations of motion and promises the possibility of investigating independently the essential space and performing dynamic simulations only in this reduced space.

A unified approach for motion and force control of robot manipulators: The operational space formulation

Abstract: A framework for the analysis and control of manipulator systems with respect to the dynamic behavior of their end-effectors is developed. First, issues related to the description of end-effector tasks that involve constrained motion and active force control are discussed. The fundamentals of the operational space formulation are then presented, and the unified approach for motion and force control is developed. The extension of this formulation to redundant manipulator systems is also presented, constructing the end-effector equations of motion and describing their behavior with respect to joint forces. These results are used in the development of a new and systematic approach for dealing with the problems arising at kinematic singularities. At a singular configuration, the manipulator is treated as a mechanism that is redundant with respect to the motion of the end-effector in the subspace of operational space orthogonal to the singular direction.

Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces

Abstract: Some materials may naturally form discontinuities such as cracks as a result of deformation. As an aid to the modeling of such materials, a new framework for the basic equations of continuum mechanics, called the "peridynamic" formulation, is proposed. The propagation of linear stress waves in the new theory is discussed, and wave dispersion relations are derived. Material stability and its connection with wave propagation is investigated. It is demonstrated by an example that the reformulated approach permits the solution of fracture problems using the same equations either on or off the crack surface or crack tip. This is an advantage for modeling problems in which the location of a crack is not known in advance.