Hamilton-Ostrogradsky approach to relativistic free spherical top dynamics. (English) Zbl 0953.70016

Matsyuk, R. Ya.

Kolář, Ivan (ed.) et al., Differential geometry and applications. Proceedings of the 7th international conference, DGA 98, and satellite conference of ICM in Berlin, Brno, Czech Republic, August 10-14, 1998. Brno: Masaryk University. 547-551 (1999).

Ostrogradsky’s approach to mechanics is rather interesting and valuable. Particularly, the formulation of generalized canonical dynamical systems which describe many processes in the real physical world, can be done better using this approach. Here the author shows that there is a possibility of constructing canonical model of free spinning particle motion in the special theory of relativity. After a brief overview of the classical spinning particle theory, the Hamiltonian dynamics of a free relativistic top is developed, which is then followed up by calculations. It is demonstrated that the Legendre transformation is equivalent to solving the Poincaré-invariant inverse problem of calculus of variations, and the corresponding Euler-Poisson expression is written out in differential form.
For the entire collection see [Zbl 0923.00021].

Reviewer: P.Achuthan (Madras)

MSC:

70H40	Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics
70H50	Higher-order theories for problems in Hamiltonian and Lagrangian mechanics
83A05	Special relativity

Keywords:

special relativity; Hamiltonian dynamics; free relativistic top; Legendre transformation; Poincaré-invariant inverse problem of calculus of variations; Euler-Poisson expression