Abstract
The paper discusses a technique for investigation of peculiar properties of invariant manifolds of conservative systems. The technique is based on constructing the envelope for the family of first integrals of such systems. Routh–Lyapunov’s method [1] has been applied for obtaining the families of invariant manifolds.
With the use of the method of envelope we have analyzed some peculiar properties of families of invariant manifolds in the problems related to rigid body dynamics and vortex theory. For the purpose of solving the computational problems arising in the process of investigations we employed the computer algebra system (CAS) Mathematica. This paper presents a development of our approach [2] to investigation of some qualitative properties of conservative systems.
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Irtegov, V., Titorenko, T. (2007). On the Peculiar Properties of Families of Invariant Manifolds of Conservative Systems. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2007. Lecture Notes in Computer Science, vol 4770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75187-8_16
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DOI: https://doi.org/10.1007/978-3-540-75187-8_16
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