Abstract
The study of Hamiltonian systems starts with the study of linear systems and the associated linear algebra. This will lead to basic results on periodic systems and variational equations of nonlinear systems.
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Notes
- 1.
Remember vectors are column vectors, but sometimes written as row vectors in the text.
- 2.
Lang’s SL 2(R) is the same as our \(Sl(2, \mathbb{R})\).
References
1982: The determination of derivatives in Brown’s lunar theory, Celest. Mech. 28, 201–07.
Weyl, H. 1948: Classical Groups, Princeton University Press, Princeton, NJ.
Yakubovich, V. A. and Starzhinskii, V. M. 1975: Linear Differential Equations with Periodic Coefficients, 1 and 2, John Wiley, New York.
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Meyer, K.R., Offin, D.C. (2017). Hamiltonian Systems. In: Introduction to Hamiltonian Dynamical Systems and the N-Body Problem. Applied Mathematical Sciences, vol 90. Springer, Cham. https://doi.org/10.1007/978-3-319-53691-0_2
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DOI: https://doi.org/10.1007/978-3-319-53691-0_2
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