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Article
A unified symmetry of lagrangian systems
In this paper, the definition and the criterion of a unified symmetry are presented. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unif...
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Article
On the Noether symmetry and Lie symmetry of mechanical systems
The Noether symmetry is an invariance of Hamilton action under infinitesimal transformations of time and the coordinates. The Lie symmetry is an invariance of the differential equations of motion under the tra...
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Article
Perturbation of symmetries of Birkhoff system and adiabatic invariants
The perturbation of symmetries of the free Birkhoff system under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of adiabatic invariants and the conditio...
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Article
Noether's theory of mechanical systems with unilateral constraints
Noether's theory of dynamical systems with unilateral constraints by introducing the generalized quasi-symmetry of the infinitesimal transformation for the transformation group G, is presented and two examples...
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Article
Lie symmetries and conserved quantities of holonomic variable mass systems
In this paper, the Lie symmetries and the conserved quantities of the holonomic variable mass systems are studied. By using the invariance of the ordinary differential equations under the infinitesimal transfo...
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Article
Equations of motion for nonholonomic mechanical systems with unilateral constraints
In this paper, the equations of motion for nonholonomic mechanical system with unilateral holonomic constraints and unilateral nonholonomic constraints are presented, and an example to illustrate the applicati...
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Article
Connections and geodesic characteristic of equations of motion for constrained mechanical systems
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 th...
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Article
Integrability for peaffian constrained systems: A geometrical theory
There exists an Ehresmann connection on the fibred constrained sub-manifold defined by Pfaffian differential constraints. It is proved that curvature of the connection is closely related to the d-σ commutation...
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Article
Stability of motion for a constrained Birkhoff's system in terms of independent variables
This paper proposes firstly the Pfaff-Birkhoff-D'Alembert's principle and obtains the equations of motion in terms of the independent variables for a constrained Birkhoff's system from the principle. Secondly,...
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Article
Stability for the equilibrium state of Chaplygin's systéms
The stability for the equilibrium states of Chaplygin's systems is considered. The equations of motion of Chaplygin's systems and the existence conditions of their equilibrium states are given. Some criteria o...
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Article
Parametric equations of nonholonomic nonconservative systems in the event space and the method of their integration
In this paper, the parametric equations with multipliers of nonholonomic nonconservative systems in the event space are established, their properties are studied, and their explicit formulation is obtained. An...
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Article
A field method for solving the equations of motion of nonholonomic systems
In this paper, the field method[1] for solving the equations of motion of holonomic nonconservative systems is extended to nonholonomic systems with constant mass and with variable mass. Two examples are given to...
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Article
Appell equations in terms of quasi-velocities and quasi-accelerations
The new forms of Appell equations in terms of quasi-velocities and quasi-accelerations for 1st order and 2nd order non-holonomic systems are presented. And the results obtained are extended to variable mass sy...
