Uniform Projectile Motion: Dynamics, Symmetries and Conservation Laws

Uniform motions in central fields

“…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.…”

“…called isotachytonic constraint. The word isotachytonic was introduced in [21] from Greek; iso = uniform; τ αχύτ ητ α = velocity. Since isotachytonic constraint represents the nonholonomic constraint nonlinear with respect to components of the velocity, it is necessary to adopt a modern approach based on the geometric concept of nonholonomic mechanical systems [6,7,9,11,13].…”

“…The bibliography in a branch of nonholonomic mechanics is very extensive and includes many important contributions and alternative geometric concepts, see [1]- [21] and references therein. It should be stressed that almost all the papers deal with the case of linear nonholonomic constraints except the several ones, e.g.…”

“…It should be stressed that almost all the papers deal with the case of linear nonholonomic constraints except the several ones, e.g. [10,12,20,21].…”

“…In this paper we apply a geometric theory of nonholonomic mechanical systems which was developed for the first order in [7] and then was generalized for the higher order case in [8]. The theory enables an investigation of different aspects of these systems; reduced equations of motion of constrained systems (equations of motion on the constraint submanifold), deformed equations of motion (deformation of original unconstrained motion equations by adding Chetaev forces), constraint symmetries and corresponding conservation laws [9] and represents a reasonable concept for an alternative mathematical treatment of concrete examples of such systems, either with linear constraints [5,20] or with nonlinear constraints [10,20,21] and even with the higher order constraints [19].…”