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Sam Hadden, Postdoctoral Fellow, Canadian Institute for Theoretical Astrophysics

Numerical integrations of the gravtational N-body problem are an essential tool in the study of planetary systems. With modern hardware and algorithms, it is possible to follow the long-term orbital evolution of planetary systems over billions of orbits. However, most known exoplanetary systems are at least ~10 to 100 times older than what can feasibly be simulated through direct numerical integration. Furthermore, incomplete knowldege of orbital parameters and masses makes comprehensive dynamical charaterization of individual systems via numerical integration intractable. Hamiltonian perturbation theory (HPT) offers a complementary approach to addressing these challenges. Rather than computing approximate solutions to the exact equations of motion, HPT provides exact or approximate solutions to approximate equations that capture the essential features of a system's dynamics. However, practical applications of HPT in planetary dynamics have typically been restricted to simple, idealized systems due to the cumbersome symbolic manipulations required to formulate theories for complicated multi-planet orbital arrangements. In this talk I will present CELMECH, an open-source code designed to streamline the application of Hamiltonian perturbation theory in planetary dynamics through computer algebra. I will also highlight the code's capabilities with some applications to realistic multi-planet systems.