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�������պ����ѧѧ�� 2006, Vol. 32 Issue (06) :742-746    DOI:
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Numerical method for Lyapunov exponents of multibody systems with constraints
Fu Shihui, Wang Qi*
School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

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ժҪ Ӧ�õ�1��Lagrange���̽����Ĵ�Լ������ϵͳ����ѧ����Ϊ������΢��-����������.�������㷨,����ת�����˳�΢�ַ�����,����ʾ�ɾ�����ʽ.���ݷ��̵��ص�,�����˷��̵�Jacobi����ľ�����ʽ,����˼���Ч��.�ڴ˻�����,������Lyapunovָ������ֵ���㷽��,��ͨ���Ծ�������κͷ����ζ���ϵͳ����Lyapunovָ����ֵ����,�����ͼ��Poincareӳ���ϵͳ�Ķ���ѧ���Խ����˷���,�����˸÷����Ŀ����Ժ���Ч��.
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Abstract�� Dynamic equations of multibody systems with constraints induced by the first kind of Lagrange’s equations are nonlinear differential-algebraic equations. To be solved numerically, nonlinear differential-algebraic equations were transformed into ordinary differential equations with the augmentation approach. Ordinary differential equations and their Jacobian matrix were given in the matrix form to improve computational efficiency. A numerical method of Lyapunov exponents of nonlinear dynamics of multibody systems was demonstrated. An example was given to analysis dynamical behavior of two multibody systems with topological tree and non-tree configuration, such as bifurcation and chaos by calculating Lyapunov exponents along with Poincare maps and phase graphs.
Keywords�� multibody system   differential-algebraic equation   Lagrange equation   Lyapunov exponent     
Received 2005-06-17;


About author: ��ʿ��(1977-), Ů, �ӱ�������, ��ʿ��,fshtp@163.com.
��ʿ��, ����.��Լ������ϵͳLyapunovָ������ֵ���㷽��[J]  �������պ����ѧѧ��, 2006,V32(06): 742-746
Fu Shihui, Wang Qi.Numerical method for Lyapunov exponents of multibody systems with constraints[J]  JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 2006,V32(06): 742-746
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