Shao-Kai Luo

Zhejiang Sci-Tech University | ZSTU · 1) Institute of Theoretical Physics; 2) Institute of Mathematical Mechanics and Mathematical Physics

The Birkhoffian, the Birkhoff's functions, the Pfaff action, the Pfaff-Birkhoff principle and the Birkhoff equations of relativistic Birkhoff systems are given. The Birkhoff representation of relativistic dynamical systems is studied. Then the theory of Noether symmetries and Lie symmetries of the relativistic Birkhoff systems is obtained by the in...

The basic integration theory of the dynamics of a rotational relativistic system is constructed. Firstly, the first integrals of the system are given. Secondly, the order of the equation of motion is reduced by using cyclic integrals and energy integrals, and thus the generalized Routh equation and generalized Whittaker equation are obtained. Third...

A field method for solving the equations of motion of a rotational relativistic Birkhoffian system is obtained. An example to illustrate the application of the method is given.

The stability problems of the relative equilibrium state manifold of nonlinear systems with nonholonomic constraints in a noninertial reference frame are addressed. First, the Routh equations of relative motion of these systems are constructed and are regarded as the relative motion of the corresponding holonomic systems. In addition, stability cri...

Only for some special nonholonomic constrained systems can a canonical Hamiltonian structure be realized. Based on a reduction of a nonholonomic system to a conditional holonomic system, a universal symplectic structure for a constrained system can be constructed in the framework of Birkhoffian generalization of Hamiltonian mechanics, which preserv...

Usually there does not exist an integral invariant of Poincar-Cartan's type for a nonholonomic system because a constraint submanifold does not admit symplectic structure in general. An integral variant of Poincar-Cartan's type, depending on the nonholonomy of the constraints and nonconservative forces acting on the system, is derived from D'Alembe...

The Birkhoffian and Birkhoff's functions of a rotational relativistic system are constructed, the Pfaff action of rotational relativistic system is defined, the Pfaff-Birkhoff principle of a rotational relativistic system is given and the Pfaff-Birkhoff-D'Alembert principles and Birkhoff's equations of rotational relativistic system are constructed...

The basic theory of relativistic Birkhoffian dynamics of rotational system is constructed, and the Birkhoffian, Birkhoff's functions, Pfaff action, Pfaff-Birkhoff principle, Pfaff-Birkhoff-D' Alembert principle and Birkhoffian equations are given. The relations among relativistic Lagrangian mechanics, Hamiltonian mechanics and relativistic Birkhoff...

The Lie symmetries and conserved quantities of the rotational relativistic holonomic and nonholonomic systems were studied. By defining the infinitestinal transformations' generators and by using the invariance of the differential equations under the infinitesimal transformations, the determining equations of Lie symmetries for the rotational relat...

The algebraic structures of the dynamical equations for the rotational relativistic systems are studied. It is found that the dynamical equations of holonomic conservative rotational relativistic systems and the special nonholonomic rotational relativistic systems have Lie's algebraic structure, and the dynamical equations of the general holonomic...

The geodesic characteristic of equations of motion for nonautonomous constrained mechanical systems is studied in the modern setting of global differential geometry. A necessary and sufficient condition for the dynamical flow of a nonautonomous mechanical system with geodesic characteristic was obtained with respect to a connection on1-jet bundle....

The theory of rotational relativistic mechanics is discussed and the theory of relativistic analytical mechanics of the rotational systems is constructed. The relativistic generalized kinetic energy function for the rotational systems Tr* = åi = 1n Ioi Gi2 (1 - Ö{1 - [(q)\dot] i2 /} Gi2 )T_r^* = \sum\limits_{i = 1}^n {I_{oi} \Gamma _i^2 (1 - \sqrt...

In this paper, the integration methods of dynamics equations of relative motion of variable mass nonlinear nonholonomic system are given such as the gradient method, the single-component method and the field method. Firstly, the dynamics equations are written in the canonical form and the field form. Secondly, the gradient method, the single-compon...

With classical variable mass and relativistic variable mass cases being considered, the relativistic D'Alembert principles of Lagrange form, Nielsen form and Appell form for variable mass controllable mechanical system are given; the relativistic Chaplygin equation. Nielsen equation and Appell equation for variable mass controllable mechanical syst...

This paper presents the integration methods for Vacco dynamics equations of nonlinear nonholonomic system. First, Vacco dynamics equations are written in the canonical form and the field form. Second, the gradient methods, the single-component methods and the field method are used to integrate the dynamics equations of the corresponding holonomic s...

The first integrals and their conditions of existence for variable mass nonholonomic system in noninertial reference frames are obtained, and the canonical equations and the variation equations of the system are extended. It is proved that using the first integral we can construct the integral invariant of the system. Finally, a series of deduction...

This paper establishes the integral theory for the dynamics of nonlinear nonholonomic system in noninertial reference frame. Firstly, based on the Routh equation of the relative motion of nonlinear nonholonomic system gives the first integral of the system. Secondly, by using cyclic integral or energy integral reduces the order of the equation and...

This paper deals with the theory of the differential invariant and integral invariant for a nonholonomic system with constraints of non-Chetaev type. It gives the restricted conditions of virtual displacement in velocity space for nonholonomic constraints of non-Chetaev type and extends the Jourdain principle and the canonical equation for the syst...

This paper presents the generalized principles of least action of variable mass nonholonomic nonconservative system in noninertial reference frame, proves the equivalence between Hölder form and Suslov form, and then obtains differential equations of motion of variable mass nonholonomic nonconservative system in noninertial reference frame.

The new Lagrangian of the relative motion of mechanical system is constructed, the variational principles of Jourdain's form of nonlinear nonholonomic nonpotential system in noninertial reference frame are established, the generalized Noether's theorem of the system above is presented and proved, and the conserved quantities of system are studied.