# American Institute of Mathematical Sciences

March  2017, 9(1): 91-130. doi: 10.3934/jgm.2017004

## Uniform motions in central fields

 1 Dept. of Mathematics, Faculty of Science, University of Ostrava, 30. dubna 22,701 03, Ostrava, Czech Republic 2 Dept. of Mathematics and Descriptive Geometry, VŠSB -Technical University of Ostrava, 17. listopadu 15,708 33, Ostrava, Czech Republic

Received  March 2016 Revised  January 2017 Published  March 2017

Fund Project: Both authors appreciate support of their departments.

We present a theoretical problem of uniform motions, i.e. motions with constant magnitude of the velocity in central fields as a nonholonomic system of one particle with a nonlinear constraint. The concept of the article is in analogy with the recent paper [21]. The problem is analysed from the kinematic and dynamic point of view. The corresponding reduced equation of motion in the Newtonian central gravitational field is solved numerically. Appropriate trajectories for suitable initial conditions are presented. Symmetries and conservation laws are investigated using the concept of constrained Noetherian symmetry [9] and the corresponding constrained Noetherian conservation law. Isotachytonic version of the conservation law of mechanical energy is found as one of the corresponding constraint Noetherian conservation law of this nonholonomic system.

Citation: Martin Swaczyna, Petr Volný. Uniform motions in central fields. Journal of Geometric Mechanics, 2017, 9 (1) : 91-130. doi: 10.3934/jgm.2017004
##### References:

show all references

##### References:
Interaction of two bodies
The initial conditions scheme
The effective potential of the Newtonian gravitational field
Infinite motions in the Newtonian gravitational field
Finite motion in the interval of distances $r\in\langle r_0,r_1\rangle$
Finite motion at the constant distance $r_0$
Finite motion in the interval of distances $r\in\langle r_1,r_0\rangle$
Comparison of trajectories: uniform vs. classical motions
Modified effective potential of the Newtonian gr. field
Classification of uniform motions in the Newtonian gr. field
Perturbed circular motions
Modified effective potential of the central field (171)
Sinusoidal spirals
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