79,802 research outputs found
The power dissipation method and kinematic reducibility of multiple-model robotic systems
This paper develops a formal connection between the power dissipation method (PDM) and Lagrangian mechanics, with specific application to robotic systems. Such a connection is necessary for understanding how some of the successes in motion planning and stabilization for smooth kinematic robotic systems can be extended to systems with frictional interactions and overconstrained systems. We establish this connection using the idea of a multiple-model system, and then show that multiple-model systems arise naturally in a number of instances, including those arising in cases traditionally addressed using the PDM. We then give necessary and sufficient conditions for a dynamic multiple-model system to be reducible to a kinematic multiple-model system. We use this result to show that solutions to the PDM are actually kinematic reductions of solutions to the Euler-Lagrange equations. We are particularly motivated by mechanical systems undergoing multiple intermittent frictional contacts, such as distributed manipulators, overconstrained wheeled vehicles, and objects that are manipulated by grasping or pushing. Examples illustrate how these results can provide insight into the analysis and control of physical systems
Variational methods, multisymplectic geometry and continuum mechanics
This paper presents a variational and multisymplectic formulation of both
compressible and incompressible models of continuum mechanics on general
Riemannian manifolds. A general formalism is developed for non-relativistic
first-order multisymplectic field theories with constraints, such as the
incompressibility constraint. The results obtained in this paper set the stage
for multisymplectic reduction and for the further development of Veselov-type
multisymplectic discretizations and numerical algorithms. The latter will be
the subject of a companion paper
Configurational temperature control for atomic and molecular systems
A new configurational temperature thermostat suitable for molecules with holonomic constraints is derived. This thermostat has a simple set of motion equations, can generate the canonical ensemble in both position and momentum space, acts homogeneously through the spatial
coordinates, and does not intrinsically violate the constraints. Our new configurational thermostat is
closely related to the kinetic temperature Nosé-Hoover thermostat with feedback coupled to the position variables via a term proportional to the net molecular force. We validate the thermostat by comparing equilibrium static and dynamic quantities for a fluid of n-decane molecules under
configurational and kinetic temperature control. Practical aspects concerning the implementation of the new thermostat in a molecular dynamics code and the potential applications are discussed
Configurational temperature control for atomic and molecular systems
A new configurational temperature thermostat suitable for molecules with holonomic constraints is derived. This thermostat has a simple set of motion equations, can generate the canonical ensemble in both position and momentum space, acts homogeneously through the spatial
coordinates, and does not intrinsically violate the constraints. Our new configurational thermostat is
closely related to the kinetic temperature Nosé-Hoover thermostat with feedback coupled to the position variables via a term proportional to the net molecular force. We validate the thermostat by comparing equilibrium static and dynamic quantities for a fluid of n-decane molecules under
configurational and kinetic temperature control. Practical aspects concerning the implementation of the new thermostat in a molecular dynamics code and the potential applications are discussed
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