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Lecture

Stellar Orbits and Potential Theory

In course

PHYS-401: Astrophysics IV : stellar and galactic dynamics

The aim of this course is to acquire the basic knowledge on specific dynamical phenomena related to the origin, equilibrium, and evolution of star clusters, galaxies, and galaxy clusters. ...

Description

This lecture covers ideal models for infinite wires and slabs, Lagrangian and Hamiltonian mechanics, orbits in spherical potentials, stellar orbits, and definitions related to trajectories and orbits. It also discusses potential theory, including the potential of infinite slabs and tightly wound spiral patterns.

Instructor

Yves Revaz

Yves Revaz is a scientist at LASTRO/EPFL. After successful studies in physics at EPFL, he accomplished his PhD entitled: "Dynamics of external regions of spiral galaxies and constraints on the dark matter", at the Geneva Observatory in the galactic dynamics group of Prof. D. Pfenniger. He then moved to the Paris Observatory to work at the LERMA (Laboratory for Studies of Radiation and Matter in Astrophysics) under the supervision of Prof. F. Combes on the understanding of cooling flows in galaxy clusters. He joined LASTRO at EPFL in 2007, where, in collaboration with Pascale Jablonka, he developed a new TreePM/SPH chemo-dynamical code called GEAR, designed to study the chemical evolution of galaxies. His current main research focus on the evolution of dwarf spheroidal galaxies and their link with the cosmology. Yves Revaz is also the author of pNbody, a parallelized python toolbox designed to manipulate large N-body systems.

Official source

Related concepts (29)

Analytical mechanics

In theoretical physics and mathematical physics, analytical mechanics, or theoretical mechanics is a collection of closely related alternative formulations of classical mechanics. It was developed by many scientists and mathematicians during the 18th century and onward, after Newtonian mechanics. Since Newtonian mechanics considers vector quantities of motion, particularly accelerations, momenta, forces, of the constituents of the system, an alternative name for the mechanics governed by Newton's laws and Euler's laws is vectorial mechanics.

Hamiltonian mechanics

Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities used in Lagrangian mechanics with (generalized) momenta. Both theories provide interpretations of classical mechanics and describe the same physical phenomena. Hamiltonian mechanics has a close relationship with geometry (notably, symplectic geometry and Poisson structures) and serves as a link between classical and quantum mechanics.

Lagrangian mechanics

In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in his 1788 work, Mécanique analytique. Lagrangian mechanics describes a mechanical system as a pair consisting of a configuration space and a smooth function within that space called a Lagrangian. For many systems, where and are the kinetic and potential energy of the system, respectively.

Hamiltonian field theory

In theoretical physics, Hamiltonian field theory is the field-theoretic analogue to classical Hamiltonian mechanics. It is a formalism in classical field theory alongside Lagrangian field theory. It also has applications in quantum field theory. The Hamiltonian for a system of discrete particles is a function of their generalized coordinates and conjugate momenta, and possibly, time. For continua and fields, Hamiltonian mechanics is unsuitable but can be extended by considering a large number of point masses, and taking the continuous limit, that is, infinitely many particles forming a continuum or field.

Hamiltonian system

A Hamiltonian system is a dynamical system governed by Hamilton's equations. In physics, this dynamical system describes the evolution of a physical system such as a planetary system or an electron in an electromagnetic field. These systems can be studied in both Hamiltonian mechanics and dynamical systems theory. Informally, a Hamiltonian system is a mathematical formalism developed by Hamilton to describe the evolution equations of a physical system.

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