Collisionless Dynamics III: The Jeans Equation Collisionless Dynamics III: The Jeans Equation.

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Collisionless Dynamics III: The Jeans Equation Collisionless Dynamics III: The Jeans Equation

Review To formulate equation of motion from: To formulate equation of motion from: F=ma, F=ma, Lagrangian ( L =T-V, n 2 nd order diff eqns), or Lagrangian ( L =T-V, n 2 nd order diff eqns), or Hamiltonian (2n 1 st order diff eqns) Hamiltonian (2n 1 st order diff eqns) Orbits follow path of least action in generalized phase space. Orbits follow path of least action in generalized phase space. If a variable does not explicitly appear in Hamil- tonian, its conjugate momentum is conserved. If a variable does not explicitly appear in Hamil- tonian, its conjugate momentum is conserved. Different types of potential have various orbit families, which can be populated differently. Different types of potential have various orbit families, which can be populated differently. Rotating potentials have Lagrange points. Rotating potentials have Lagrange points.

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