Abstract
Recently, the application of Hamilton’s Law of Varying Action to initial value problems in dynamics has been generalized and simplified. With our new Integral Variation method, approximate solutions can be constructed to arbitrary initial value problems involving systems of first-order ordinary differential equations. First, this new constructive technique is briefly described. Then the method is illustrated with two example problems: 1. the damped oscillator (two linear differential equations), and 2. the Lagrange planetary equations with zonal harmonics and drag (a highly nonlinear system of six coupled first-order differential equations). Numerical results confirm that the Integral Variation method indeed provides accurate approximate analytical solutions over a specified finite time interval.
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© 1985 D. Reidel Publishing Company
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Hitzl, D.L., Zele, F. (1985). Recent Extensions of Hamilton’s Law of Varying Action with Applications — The Integral Variation Method. In: Szebehely, V.G. (eds) Stability of the Solar System and Its Minor Natural and Artificial Bodies. NATO ASI Series, vol 154. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5398-7_17
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DOI: https://doi.org/10.1007/978-94-009-5398-7_17
Publisher Name: Springer, Dordrecht
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