Abstract
Until recently, it had been thought that the equation of motion of classical systems with dissipative forces could not be derived from a Lagrangian function by a pure variational procedure. The dissipative terms of the equation were usually introduced directly in the Lagrange’s equation through a Rayleigh dissipative function or by using complex coordinates and velocities in the Lagrangian. Recently,1,2 a pure Lagrangian description was found for the linearly damped oscillator and certain dynamical systems with velocity-dependent forces and a Hamilton-Jacobi treatment was developed3 for these systems. We extend these results to the general class of classical systems with one degree of freedom governed by a Lienard equation of motion which is of the form
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© 1980 Springer-Verlag Wien
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Riccia, G.D. (1980). A Hamilton-Jacobi Treatment of Dissipative Systems with one Degree of Freedom. In: Blaquiére, A., Fer, F., Marzollo, A. (eds) Dynamical Systems and Microphysics. International Centre for Mechanical Sciences, vol 261. Springer, Vienna. https://doi.org/10.1007/978-3-7091-4330-8_19
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DOI: https://doi.org/10.1007/978-3-7091-4330-8_19
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-81533-5
Online ISBN: 978-3-7091-4330-8
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