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The constants of motion of the following systems are deduced: a relativisticparticle with linear dissipation, a no-relativistic particle with a timeexplicitly depending force, a no-relativistic particle with a constant forceand time depending mass, and a relativistic particle under a conservative forcewith position depending mass. The problem of getting the Hamiltonian for thesesystems is determined by getting the velocity as an explicit function ofposition and generalized linear momentum, and this problem can be solved afirst approximation for the first above system.Comment: 15 pages, Te

Constants of Motion for Several One-Dimensional Systems and Problems Associated with Getting Their Hamiltonians