Open AccessUniform motions in central fields
Author(s) -
Martin Swaczyna,
Petr Volný
Publication year - 2017
Publication title -
journal of geometric mechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.511
H-Index - 17
eISSN - 1941-4897
pISSN - 1941-4889
DOI - 10.3934/jgm.2017004
Subject(s) - nonholonomic system , conservation law , noetherian , classical mechanics , constraint (computer aided design) , conservation of energy , symmetry (geometry) , kinematics , mathematics , equations of motion , nonlinear system , homogeneous space , newtonian fluid , physics , mathematical analysis , geometry , computer science , algebra over a field , pure mathematics , quantum mechanics , artificial intelligence , robot , thermodynamics , mobile robot
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.Web of Science911309