2013
DOI: 10.1103/physrevlett.110.174301
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Classical Mechanics of Nonconservative Systems

Abstract: Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often goes unnoticed in physics: it is formulated as a boundary value problem in time but is used to derive equations of motion that are solved with initial data. This subtlety can have undesirable effects. I present a formulation of Hamilton's principle that is compatible with ini… Show more

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Cited by 206 publications
(324 citation statements)
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“…We extended the formalism in [63,64] to incorporate finite-size effects, and computed the spin-spin contributions to the acceleration and spin evolution to 4.5PN order from first principles, without resorting to balance equations. To our knowledge, the calculation of finite-size effects in radiation reaction had not been carried out until now.…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…We extended the formalism in [63,64] to incorporate finite-size effects, and computed the spin-spin contributions to the acceleration and spin evolution to 4.5PN order from first principles, without resorting to balance equations. To our knowledge, the calculation of finite-size effects in radiation reaction had not been carried out until now.…”
Section: Discussionmentioning
confidence: 99%
“…We achieve this using the EFT framework for spinning bodies [61] extended to nonconservative systems [53,54,[62][63][64]. At 4.5PN order, the computations are independent of the spin supplementary condition.…”
Section: Introductionmentioning
confidence: 99%
“…It states that for a discrete system with total mechanical power W as in (1) and dissipation potential R that obeys (2) 2 the true velocityq traversing a given configuration q is such that the reduced dissipation potential R := R − W is stationary with respect to all virtual variations δq once the generalized forces δL δq are held fixed. 1 In conclusion, I have shown that a generalized dissipation potential derived from a (non necessarily quadratic) dissipation function can be set as the basis of the Rayleigh-Lagrange dynamics of a discrete system, which may thus remain a viable alternative to the approach proposed in [1]. The method suggested in this Comment is likely to be extended to continuum systems along the lines followed in the monograph [2] for the classical quadratic case.…”
mentioning
confidence: 95%
“…02.30.Jr Dissipative systems are ubiquitous in physics but their description in general mathematical terms is still a debated issue. Galley [1] proposed a general approach to the motion of a discrete dissipative system based on a modified Hamilton principle, which remedies the timereversibility of the Lagrange equations, which express the stationarity of the classical action. The major conceptual drift for developing this method was the supposed inability of the classical Rayleigh equations to account for resistive forces more general than linear functions in the velocities.…”
mentioning
confidence: 99%
“…The explicit time dependence of the Lagrangian and Hamiltonian operators introduces a major difficulty in this study since the canonical commutation relations are not preserved in time. Different approaches have been used in order to apply the canonical quantization scheme to dissipative systems [10][11][12][13][14][15].…”
Section: Introductionmentioning
confidence: 99%