A new mathematical construction of the general nonlinear ODEs of motion in rigid body dynamics (Euler's equations)

作者：Panayotounakos Dimitrios E; Rizou Ioanna; Theotokoglou Efstathios E^*

来源：Applied Mathematics and Computation, 2011, 217(21): 8534-8542.

DOI：10.1016/j.amc.2011.03.057

• Rigid body dynamics
• Nonlinear ODEs
• New mathematical construction
• Euler's equations
• Abel equations of the second kind

It is shown that the three nonlinear dynamic Euler ordinary differential equations (ODEs), concerning the motion of a rigid body free to rotate about a fixed point, are reduced, by means of a subsidiary function which is to be determined, to three Abel equations of the second kind of the normal form. Based on a recently developed mathematical construction concerning exact analytic solutions of the Abel nonlinear ODEs of the second kind, we perform a new mathematical solution for the classical dynamic Euler nonlinear ODEs.

• 出版日期2011-7-1