Phys. Rev. E 53, 1890–1899 (1996)Nonconservative Lagrangian and Hamiltonian mechanicsReceived 14 September 1995; published in the issue dated February 1996 Traditional Lagrangian and Hamiltonian mechanics cannot be used with nonconservative forces such as friction. A method is proposed that uses a Lagrangian containing derivatives of fractional order. A direct calculation gives an Euler-Lagrange equation of motion for nonconservative forces. Conjugate momenta are defined and Hamilton’s equations are derived using generalized classical mechanics with fractional and higher-order derivatives. The method is applied to the case of a classical frictional force proportional to velocity. © 1996 The American Physical Society. © 1996 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.53.1890
DOI:
10.1103/PhysRevE.53.1890
PACS:
03.20.+i, 46.10.+z, 46.30.Pa
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