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Abstract The two-dimensional classical system with dissipation forces in the form of damping proportional to the velocity squared is considered. It is demonstrated that, owing to the existence of a first integral fixing the velocity direction, the dynamics can be restricted to the analysis of rectilinear paths. This reduction of Newton’s original system maintains the fundamental properties of the dissipative force under consideration. Based on this result, it is demonstrated that such a reduced system can be effectively treated as a two-dimensional Hamiltonian system with a position-dependent mass, which can also exhibit anisotropy. This result is derived by applying the Hamiltonization procedure based on the Jacobi last multiplier (JLM) method combined with a Legendre transform. The obtained result is then used to investigate the coherent backscattering phenomenon in the open Sinai billiard.
Pigoń et al. (Mon,) studied this question.