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1.
Lyapunov's first method, extended by V. V. Kozlov to nonlinear mechani- cal systems, is applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conservative and dissipative forces. The mo- tion of the system is limited by ideal nonlinear nonholonomic constraints. Five cases determined by the relationship between the degree of the first nontrivial polynomials in Maclaurin's series for the potential energy and the functions that can be generated from the equations of nonlinear nonholonomic constraints are analyzed. In the three eases, the theorem on the instability of the position of equilibrium of nonholonomic systems with linear homogeneous constraints (V. V. Kozlov (1986)) is generalized to the case of nonlin- ear nonhomogeneous constraints. In the other two cases, new theorems are set extending the result from V. V. Kozlov (1994) to nonholonomic systems with nonlinear constraints. 相似文献
2.
Thestudyofconservationlawsofdynamicalsystemisasignificantaspectofmodernanalyticalmechanics.In1918,usingtheinvarianceofHamiltonactionundertheinfinitesimaltransformations,Noether[1]studiedconservationlawsofmechanicalsystemandpresentedthefamousNoether’stheor… 相似文献
3.
One type of integrals for the equations of motion of higher-order nonholonomic systems 总被引:1,自引:0,他引:1
梅凤翔 《应用数学和力学(英文版)》1991,12(8):799-806
This paper presents one type of integrals and its condition of existence for theequations Of motion of higher-order nonholonomic systems,including I-order integral(generalized energy integral),2-order integral and p-order integral(P>2).All of theseintegrals can be constructed by the Lagrangianfunction of the system.Two examples aregiven to illustrate the application of the suggested method. 相似文献
4.
IntroductionThemotionofamechanicalsystemwithunilateralconstraintsismoregeneralthanwithbilateralconstraints1andyetitsinvestigationismoredifficult[1,2].Thesystemswithunilateralconstraintsinvolvetheholonomicmechanicalsystemswithunilateralholonomicconstraints[3~6]andthenonholonondcmeChanicalsystemswithunilateralholonondcconstraintS[7]andthenonholonondcmechanicalsystemswithunilateralnonholonondcconstraintS[2]andsoon.ThispaperstUdiesatypeofmoregeneralsystemswithunilateralconstfaints:nonholonondcs… 相似文献
5.
罗绍凯 《应用数学和力学(英文版)》1993,14(10):907-918
This paper establishes the integral theory for the dynamics of nonlinearnonholonomic system in noninertial reference frame.Firstly,based on the Routhequation of the relative motion of nonlinear nonholonomic system gives the firstintegral of the system.Secondly,by using cyclic integral or energy integral reduces theorder of the equation and obtains generalized Routh equation and Whittaker equationrespectively.Thirdly,derives canonical equation and variation equation and by usingthe first integral constructs integral invariant.And then,establishes the basic integralvariants and the integral invariant of Poincare-Cartan type.Finally,we give a series ofdeductions. 相似文献
6.
The new variational principle of Gauss’s form of nonlinear nonholonomicnonpotential system relative to non-inertial reference frame is established byconstructing generalized inertial potentials.Noether’s theorem and Noether’s inversetheorem of the system above is presented and proved.Finally,one example is given toillustrate the application. 相似文献
7.
The work analyzes energy relations for nonholonomic systems, whose motion is restricted by nonlinear nonholonomic constraints. For the mechanical systems with linear constraints, the analysis of energy relations was carried out in [1], [2], [3], [4], [5], [6] …. On the basis of corresponding Lagrange’s equations, a general law of the change in energy dε/dt is formulated for mentioned systems by the help of which it is shown that there are two types of the laws of conservation of energy, depending on the structure of elementary work of the forces of constraint reactions. Also, the condition for existing the second type of the law of conservation of energy is formulated in the form of the system of partial differential equations. The obtained results are illustrated by a model of nonholonomic mechanical system. 相似文献
8.
AMETHODFORSOLVINGTHEDYNAMICSOFMULTIBODYSYSTEMSWITHRHEONOMICANDNONHOLONOMICCONSTRAINTS¥ShuiXiaoping(水小平)ZhangYongfa(张永发)(Depar... 相似文献
9.
Robust adaptive control of nonholonomic systems in chained form with linearly parameterized and strongly nonlinear disturbance and drift terms is dicussed. The novelty of the proposed method is a combined use of the state-scaling and the back-stepping procedure. 相似文献
10.
ON THE STABILITY OF NONHOLONOMIC MECHANICAL SYSTEMS WITH RESPECT TO PARTIAL VARIABLES 总被引:4,自引:2,他引:2
ONTHESTABILITYOFNONHOLONOMICMECHANICALSYSTEMSWITHRESPECTTOPARTIALVARIABLESZhuHai-ping(朱海平)MeiFeng-xiang(梅凤翔)(BeijingUniversit... 相似文献
11.
乔永芬 《应用数学和力学(英文版)》1990,11(10):973-983
In this paper,the Gibbs-Appell’s equations of motion are extended to the most generalvariable mass nonholonomic mechanical systems.Then the Gibbs-Appell’s equations ofmotion in terms of generalized coordinates or quasi-coordinates and an integral variationalprinciple of variable mass nonlinear nonholonomic mechanical systems are obtained.Finally,an example is given. 相似文献
12.
李刚常 《应用数学和力学(英文版)》1998,19(2):135-146
I.IntroductionSinceE.T.Whittaker.proposedfoestabilit}'problellll'lofnonholononlicsystemsin1904forthefirsttime,thescholarsathomeandabroad11a\'emadealotofresearchesontheequilibriunlstabilityoflinearand11olllinearnonllolollolnicsystems,andhaveobtainedaseriesofimportantresultslZ--7].Hobbled'er,theexpositionandapplicationrelatedtoLagrange'stheorenlinthestabilityanalysisfornonholonomicsystemsisseldonlseenuptonow.Althoughitwasmentionedinreference[3].aspecialdiscussionhasnotbeencarriedoutyet.Asafam… 相似文献
13.
Mei Fengxiang 《Acta Mechanica Sinica》1989,5(3):260-268
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.
The project supported by the National Natural Science Foundation of China. 相似文献
14.
The paper proposes computer algebra system (CAS) algorithms for computer-assisted derivation of the equations of motion for
systems of rigid bodies with holonomic and nonholonomic constraints that are linear with respect to the generalized velocities.
The main advantages of using the D’Alembert-Lagrange principle for the CSA-based derivation of the equations of motion for
nonholonomic systems of rigid bodies are demonstrated. Among them are universality, algorithmizability, computational efficiency,
and simplicity of deriving equations for holonomic and nonholonomic systems in terms of generalized coordinates or pseudo-velocities
__________
Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 106–115, September 2006. 相似文献
15.
16.
Noether’stheoremrevealstheinnerconnectionbetweentheconservationlawsandthedynamicalsymmetryofdynamicalsystems.Intherecenttwent... 相似文献
17.
In this paper, we prove that for holonomic nonconservative dynamical system the Poincaré and Poincaré-Cartan integral invariants
do not exist. Instead of them, we introduce the integral variants of Poincaré-Cartan's type and of Poincare's type for holonomic
nonconservative dynamical systems, and use these variants to solve the problem of nonlinear vibration. We also prove that
the integral invariants introduced in references [1] and [2] are merely the basic integral variants given by this paper.
Project supported by National Natural Science Foundation of China 相似文献
18.
Parametric equations of nonholonomic nonconservative systems in the event space and the method of their integration 总被引:1,自引:0,他引:1
Mei Fengxiang 《Acta Mechanica Sinica》1990,6(2):160-168
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.
The Project is supported by the National Natural Science Foundation of China. 相似文献
19.
In this paper, the new forms of the differential equations of motion of the systems with higher-order nonholonomic constraints are obtained at first, and then the equivalence between these equations and the known equations is demonstrated. Finally an example is given to illustrate the application of our new equations. 相似文献
20.
罗绍凯 《应用数学和力学(英文版)》1998,19(1):45-57
I'IntroductionThespinningmotionisintrinsicattributeofmicroscopicparticle.In1979,R.BengtssonandS.Frauendorfaccuratlymeasuredthemaximumvolumesofthespinningrotativevelocityof14kindsofnucleons,andtheresultsshowedthatthemaximumvolumesofthespinningrotativevelocityofeachnucleonaredifferent[ll.Withthede\'elopingofmodernscienceandtechnology,moreandmoreexperimentalfactsrelatedtothehighspeedrotationquestions,theEinstein'srelativitytheoryandtherotationaltheoryofclassicalmechanicsarenotsuitabletothesepro… 相似文献