scholarly journals GEOMETRIC HAMILTON–JACOBI THEORY FOR NONHOLONOMIC DYNAMICAL SYSTEMS

2010 ◽  
Vol 07 (03) ◽  
pp. 431-454 ◽  
Author(s):  
JOSÉ F. CARIÑENA ◽  
XAVIER GRÀCIA ◽  
GIUSEPPE MARMO ◽  
EDUARDO MARTÍNEZ ◽  
MIGUEL C. MUÑOZ-LECANDA ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Symplectic Structure ◽  
Free Particle ◽  
Nonholonomic Constraints ◽  
Lagrangian Function ◽  
Constants Of Motion ◽  
Geometric Formulation ◽  
Complete Solutions ◽  
Nonholonomic Dynamical Systems

The geometric formulation of Hamilton–Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton–Jacobi problem with the symplectic structure defined from the Lagrangian function and the constraints is studied. The concept of complete solutions and their relationship with constants of motion, are also studied in detail. Local expressions using quasivelocities are provided. As an example, the nonholonomic free particle is considered.

Equations of Motion for Nonholonomic, Constrained Dynamical Systems via Gauss’s Principle

1993 ◽  
Vol 60 (3) ◽  
pp. 662-668 ◽  
Author(s):  
R. E. Kalaba ◽  
F. E. Udwadia
Keyword(s):  
Dynamical Systems ◽  
Closed Form ◽  
Programming Problem ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Closed Form Solution ◽  
Nonholonomic Constraints ◽  
Form Solution ◽  
Constrained Motion ◽  
Constraint Forces

In this paper we develop an analytical set of equations to describe the motion of discrete dynamical systems subjected to holonomic and/or nonholonomic Pfaffian equality constraints. These equations are obtained by using Gauss’s Principle to recast the problem of the constrained motion of dynamical systems in the form of a quadratic programming problem. The closed-form solution to this programming problem then explicitly yields the equations that describe the time evolution of constrained linear and nonlinear mechanical systems. The direct approach used here does not require the use of any Lagrange multipliers, and the resulting equations are expressed in terms of two different classes of generalized inverses—the first class pertinent to the constraints, the second to the dynamics of the motion. These equations can be numerically solved using any of the standard numerical techniques for solving differential equations. A closed-form analytical expression for the constraint forces required for a given mechanical system to satisfy a specific set of nonholonomic constraints is also provided. An example dealing with the position tracking control of a nonlinear system shows the power of the analytical results and provides new insights into application areas such as robotics, and the control of structural and mechanical systems.

Influence of nonholonomic constraints on variations, symplectic structure, and dynamics of mechanical systems

2007 ◽  
Vol 48 (8) ◽  
pp. 082901 ◽  
Author(s):  
Yong-Xin Guo ◽  
Shi-Xing Liu ◽  
Chang Liu ◽  
Shao-Kai Luo ◽  
Yong Wang
Keyword(s):  
Symplectic Structure ◽  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Structure And Dynamics

scholarly journals U DUALITY AND CENTRAL CHARGES IN VARIOUS DIMENSIONS REVISITED

1998 ◽  
Vol 13 (03) ◽  
pp. 431-492 ◽  
Author(s):  
LAURA ANDRIANOPOLI ◽  
RICCARDO D'AURIA ◽  
SERGIO FERRARA
Keyword(s):  
Symplectic Structure ◽  
Special Geometry ◽  
Geometric Formulation ◽  
Extended Theories

A geometric formulation which describes extended supergravities in any dimension in the presence of electric and magnetic sources is presented. In this framework, the underlying duality symmetries of the theories are manifest. Particular emphasis is given to the construction of central and matter charges and to the symplectic structure of all D=4, N-extended theories. The latter may be traced back to the existence, for N>2, of a flat symplectic bundle which is the N>2 generalization of N=2 Special Geometry.

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