Lyapunov-Kozlov method for singular cases

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Lyapunov-Kozlov method for singular cases水利论文2L [p)gF^

i}0mJ L,_p h0Abstract:Lyapunov's first method,extended by Kozlov to nonlinear mechanical systems,is applied to study the instability of the equilibrium position of a mechanical system moving in the field of conservative and dissipative forces.The cases with a tensor of inertia or a matrix of coefficients of the Rayleigh dissipative function are analyzed singularly in the equilibrium position.This fact renders the impossible application of Lyapunov's approach in the analysis of the stability because,in the equilibrium position,the conditions of the existence and uniqueness of the solutions to the differential equations of motion are not fulfilled.It is shown that Kozlov's generalization of Lyapunov's first method can also be applied in the mentioned cases on the conditions that,besides the known algebraic expression,more are fulfilled.Three theorems on the instability of the equilibrium position are formulated.The results are illustrated by an example.水利论文? @ NZ+|7X:m

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OvST0m1t7~O'm0Faculty of Mechanical Engineering, University of Belgrade,Kraljice Marije 16, Belgrade 11000, SerbiaFaculty of Mechanical Engineering, University of Kragujevac,Dositejeva 19, Kraljevo 36000, Serbia

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期 刊:

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应用数学和力学(英文版)

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Journal:

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;]:[:pDi Y?0Applied Mathematics and Mechanics

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年,卷(期):

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{0[:e4l)C,^5}-WS02011, 32(9)水利论文o Zk'z&LVK`e

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instability

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F+v?.~[(X[,}0singular case水利论文,i-KC-e8x5C!Y

F(hRK!]E0asymptotic motion水利论文 v \'S l rM3`G'By

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dissipative force

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gyu"qh _^$LT1L0Lyapunov existence and uniqueness moving in the field equations of motion mechanical systems application solutions Rayleigh function extended approach analysis results matrix study fact

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