Mei symmetry and generalized Hojman conserved quantity for variable mass systems with unilateral holonomic constraints

This paper studies Mei symmetry which leads to a generalized Hojman conserved quantity for variable mass systems with unilateral holonomic constraints. The differential equations of motion for the systems are established, the definition and criterion of the Mei symmetry for the systems are given. The necessary and sufficient condition under which the Mei symmetry is a Lie symmetry for the systems is obtained and a generalized Hojman conserved quantity deduced from the Mei symmetry is got. An example is given to illustrate the application of the results.

ARBITRARILY HIGH-ORDER ENERGY-CONSERVING METHODS FOR HAMILTONIAN PROBLEMS WITH QUADRATIC HOLONOMIC CONSTRAINTS

In this paper,we define arbitrarily high-order energy-conserving methods for Hamilto-nian systems with quadratic holonomic constraints.The derivation of the methods is made within the so-called line integral framework.Numerical tests to illustrate the theoretical findings are presented.

ENERGY AND QUADRATIC INVARIANTS PRESERVING METHODS FOR HAMILTONIAN SYSTEMS WITH HOLONOMIC CONSTRAINTS

We introduce a new class of parametrized structure–preserving partitioned RungeKutta(α-PRK)methods for Hamiltonian systems with holonomic constraints.The methods are symplectic for any fixed scalar parameterα,and are reduced to the usual symplectic PRK methods like Shake-Rattle method or PRK schemes based on Lobatto IIIA-IIIB pairs whenα=0.We provide a new variational formulation for symplectic PRK schemes and use it to prove that theα-PRK methods can preserve the quadratic invariants for Hamiltonian systems subject to holonomic constraints.Meanwhile,for any given consistent initial values(p0,q0)and small step size h>0,it is proved that there existsα∗=α(h,p0,q0)such that the Hamiltonian energy can also be exactly preserved at each step.Based on this,we propose some energy and quadratic invariants preservingα-PRK methods.Theseα-PRK methods are shown to have the same convergence rate as the usual PRK methods and perform very well in various numerical experiments.

Modeling and Finite-Time Tracking Control for Mobile Manipulators with Affine and Holonomic Constraints

This paper focuses on the problem of modeling and finite-time tracking control for mobile manipulators with affine and holonomic constraints. A reduced dynamic model is obtained by appropriately processing anne and holonomic constraints, respectively. Then finite-time tracking controllers are designed to ensure that output tracking errors of closed-loop system converge to zero in finite time while the constraint force remains bounded. Finally, detailed simulation results are provided to confirm the effectiveness of the control strategy.

Structural Equation and Mei Conserved Quantity of Mei Symmetry for Appell Equations in Holonomic Systems with Unilateral Constraints

Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomie mechanic systems with unilateral constraints axe established. The definition and the criterion of Mei symmetry for Appell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups axe also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results.

A type of new conserved quantity deduced from Mei symmetry for Nielsen equations in a holonomic system with unilateral constraints

A type of new conserved quantity deduced from Mei symmetry for Nielsen equations in a holonomic system with unilateral constraints is investigated. Nielsen equations and differential equations of motion for the holonomic mechanical system with unilateral constraints are established. The definition and the criterion of Mei symmetry for Nielsen equations in the holonomic systems with unilateral constraints under the infinitesimal transformations of Lie group are also given. The expressions of the structural equation and a type of new conserved quantity of Mei symmetry for Nielsen equations in the holonomic system with unilateral constraints are obtained. An example is given to illustrate the application of the results.

On Mechanical Property of Constraint

In this paper. the mechanical properties of holonomic systems and mon-holonomicsystems are strdied. This is an important and urgent problem.

Constrained Fractional Variational Problems of Variable Order

Isoperimetric problems consist in minimizing or maximizing a cost functional subject to an integral constraint.In this work, we present two fractional isoperimetric problems where the Lagrangian depends on a combined Caputo derivative of variable fractional order and we present a new variational problem subject to a holonomic constraint. We establish necessary optimality conditions in order to determine the minimizers of the fractional problems. The terminal point in the cost integral,as well as the terminal state, are considered to be free, and we obtain corresponding natural boundary conditions.

Kinematic Control of Wheeled Snake-Like Mobile Robot

From a bionics viewpoint , this paper proposes a mechanical model of a wheeled snake like mobile mechanism. On the hypothesis of the existing non holonomic constraints on the robot kinematics, we set up the relationship among the kinetic control parameters in the snake like movement using Lie group and Lie algebra of the principle fiber bundle and provide some theoretical control methods to realize the snake like locomotion.