Publication details
Motion in central gravitational field with Schwarzschild metric as a non-holonomic system with non-linear constraint: Geometrical setting
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Periodical |
| Magazine / Source | International Journal of Non-Linear Mechanics |
| MU Faculty or unit | |
| Citation | |
| Web | Full Text |
| Doi | http://dx.doi.org/10.1016/j.ijnonlinmec.2019.03.009 |
| Keywords | non-linear mechanics; constrained systems; geometrical theory on fibred manifolds; Schwarzschild metric |
| Description | Mechanical systems with non-holonomic constraints are often studied in technical applications. In such situations linear or affine non-holonomic constraints are usually relevant. On the other hand, there exist mechanical systems which can be naturally interpreted as non-holonomic ones with non-linear constraint. Such systems occur typically in the theory of relativity. Within physical theories they are standardly described by physical methods, not as systems subjected to non-holonomic constraints. Nevertheless, every non-holonomic system can be treated by a universal purely mathematical approach — geometrical theory on fibred manifolds with Chetaev type constraint submanifolds. For describing all aspects of a system behaviour, including all symmetries and conservation laws, it is sufficient to have the corresponding unconstrained Lagrangian and the constraint. No additional physical assumptions are needed. We demonstrate this for a typical physical system with a non-linear non-holonomic constraint — a relativistic particle moving in central field of a non-rotating star. Within the geometrical theory we obtain constraint equations of motion and their solution. Especially, we obtain equations or constraint symmetries, their solution for coordinate transformations, and corresponding conservation laws from general relations obtained on the base of this universal geometrical theory. |