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Potentials of arbitrary forces with fractional derivatives. (English) Zbl 1080.70516
Summary: The Laplace transform of fractional integrals and fractional derivatives is used to develop a general formula for determining the potentials of arbitrary forces, conservative and nonconservative, in order to introduce dissipative effects (such as friction) into Lagrangian and Hamiltonian mechanics. The results are found to be in exact agreement with Riewe’s results for special cases. Illustrative examples are given.
MSC:
70H03Lagrange’s equations
70H05Hamilton’s equations
26A33Fractional derivatives and integrals (real functions)