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Hamiltonian Dynamical Systems and Applications pp 367–390Cite as

The calculus of variations and the forced pendulum

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Part of the book series: NATO Science for Peace and Security Series ((NAPSB))

Consider the equation of forced pendulum type: u "+ Vu (t,u) = 0 (*) where' = d/dt and V is smooth and 1-periodic in its arguments. We will show how to use elementary minimization arguments to find a variety of solutions of (*). We begin with periodic solutions of (*) and then find heteroclinic solutions making one transition between a pair of periodics. Then we construct heteroclinics and homoclinics making multiple (even infinitely many) transitions between periodics. If time permits, we may also discuss the construction of related mountain pass orbits of (*).

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin-Madison, 53706-1388, Madison, MI, USA

    Paul H. Rabinowitz

Authors
  1. Paul H. Rabinowitz
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Editors and Affiliations

  1. McMaster University, L8S 4K1, Hamilton, ON, Canada

    Walter Craig

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© 2008 Springer Science + Business Media B.V

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Rabinowitz, P.H. (2008). The calculus of variations and the forced pendulum. In: Craig, W. (eds) Hamiltonian Dynamical Systems and Applications. NATO Science for Peace and Security Series. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6964-2_15

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