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Uniform projectile motion: Dynamics, symmetries and conservation laws. (English) Zbl 1308.70017
Summary: A geometric nonholonomic theory is applied to the problem of uniform projectile motion, i.e. motion of a projectile with constant instantaneous speed. The problem is investigated from the kinematic and dynamic point of view. Corresponding kinematic parameters of classical and uniform projectile motion are compared, nonholonomic Hamilton equations are derived and their solvability is discussed. Symmetries and conservation laws of the considered system are studied, the nonholonomic formulation of a conservation law of generalized energy is found as one of the corresponding Noetherian first integrals of this nonholonomic system.

MSC:
70F25 Nonholonomic systems related to the dynamics of a system of particles
70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
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