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  • 1
    Electronic Resource
    Electronic Resource
    Perturbation of symmetries of Birkhoff system and adiabatic invariants (2000)
    Springer
    Acta mechanica Sinica 16 (2000), S. 282-288 
    Details
    ISSN: 1614-3116
    Keywords: Birkhoff system ; symmetry ; perturbation ; adiabatic invariants
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract 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 conditions for their existence are given. Then these results are generalized to the constrained Birkhoff system. One example is presented to illustrate these results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02487669
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  • 2
    Electronic Resource
    Electronic Resource
    Parametric equations of nonholonomic nonconservative systems in the event space and the method of their integration (1990)
    Springer
    Acta mechanica Sinica 6 (1990), S. 160-168 
    Details
    ISSN: 1614-3116
    Keywords: event space ; nonholonomic nonconservative system ; parametric equation ; integration method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract 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. And then the field method for integrating these equations is given. Finally, an example illustrating the application of the integration method is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02488447
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  • 3
    Electronic Resource
    Electronic Resource
    Integrability for peaffian constrained systems: A geometrical theory (1998)
    Springer
    Acta mechanica Sinica 14 (1998), S. 85-91 
    Details
    ISSN: 1614-3116
    Keywords: nonholonomic constraints ; Frobenius integrability ; fibre bundle ; Ehresmann connections ; curvature form
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract 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 relation in the classical nonholonomic mechanics. It is also proved that conditions of complete integrability for Pfaffian systems in Frobenius sense are equivalent to the three requirements upon the conditional variations in the classical calculus of variations: (1) the variations belong to the constrained manifold, (2) variational operators commute with differential operators, (3) variations satisfy the Chetaev's conditions. Thus this theory verifies the conjecture or experience of researchers of mechanics on the integrability conditions in terms of variation calculus.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02486834
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  • 4
    Electronic Resource
    Electronic Resource
    Appell equations in terms of quasi-velocities and quasi-accelerations (1987)
    Springer
    Acta mechanica Sinica 3 (1987), S. 268-277 
    Details
    ISSN: 1614-3116
    Keywords: quasi-velocity ; quasi-acceleration ; non-holonomic system ; variable mass system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract 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 systems. Finally an example is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02486773
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  • 5
    Electronic Resource
    Electronic Resource
    A field method for solving the equations of motion of nonholonomic systems (1989)
    Springer
    Acta mechanica Sinica 5 (1989), S. 260-268 
    Details
    ISSN: 1614-3116
    Keywords: nonholonomic system ; variable mass system ; method of integration ; field method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract 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 illustrate its application.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02487988
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  • 6
    Electronic Resource
    Electronic Resource
    Stability for the equilibrium state of Chaplygin's systéms (1995)
    Springer
    Applied mathematics and mechanics 16 (1995), S. 635-642 
    Details
    ISSN: 1573-2754
    Keywords: analytic mechanics ; nonholonomic system ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract 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 of stability for the equilibrium. states of Chaplygin's systems are obtained. Two examples are finally given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02455247
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  • 7
    Electronic Resource
    Electronic Resource
    Stability of motion for a constrained Birkhoff's system in terms of independent variables (1997)
    Springer
    Applied mathematics and mechanics 18 (1997), S. 55-60 
    Details
    ISSN: 1573-2754
    Keywords: dynamics ; Birkhoff's system ; stability of motion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract 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, it establishes the equations of perturbation of the system. Finally, it obtains the stability criteria by using the Liapunov direct method and the firstly approximate method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02457501
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  • 8
    Electronic Resource
    Electronic Resource
    Connections and geodesic characteristic of equations of motion for constrained mechanical systems (1998)
    Springer
    Applied mathematics and mechanics 19 (1998), S. 837-842 
    Details
    ISSN: 1573-2754
    Keywords: 1-jet bundle ; dynamical flow ; vertical endomorphism ; connection ; geodesic
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract 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 dynamical flow concerning the non-autonomous case was always of geodesic characteristic with regard to torsion-free connections. Thus the motion of any nonautomomous mechanical system with constraints can be always represented by the motion along the geodesic line of torsion-free connection on1-jet bundle, which is different from the case in an autonomous mechaincal system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458238
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  • 9
    Electronic Resource
    Electronic Resource
    Equations of motion for nonholonomic mechanical systems with unilateral constraints (1999)
    Springer
    Applied mathematics and mechanics 20 (1999), S. 59-67 
    Details
    ISSN: 1573-2754
    Keywords: analytical mechanics ; unilateral constraint ; nonholonomic system ; equation of motion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract 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 application of the result is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459274
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  • 10
    Electronic Resource
    Electronic Resource
    Lie symmetries and conserved quantities of holonomic variable mass systems (1999)
    Springer
    Applied mathematics and mechanics 20 (1999), S. 629-634 
    Details
    ISSN: 1573-2754
    Keywords: analytical mechanics ; variable mass ; Lie symmetry ; conserved quantity ; O316
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract 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 transformations, the determining equations and the conserved quantities are given. And an example is given to illustrate the application of the result.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02464935
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