Collisionless Dynamics Collisionless Dynamics III:III:

The Jeans EquationThe Jeans Equation

ReviewReview To formulate equation of motion from:To formulate equation of motion from:

F=maF=ma, , Lagrangian Lagrangian ((LL=T-V, =T-V, nn 2 2ndnd order diff eqns), or order diff eqns), or HamiltonianHamiltonian (2 (2nn 1 1stst order diff eqns) order diff eqns)

Orbits follow path of least action in Orbits follow path of least action in generalized phase space.generalized phase space.

If a variable does not explicitly appear in If a variable does not explicitly appear in Hamil-tonian, its conjugate momentum is Hamil-tonian, its conjugate momentum is conservedconserved..

Different types of potential have various Different types of potential have various orbit orbit familiesfamilies, which can be populated differently., which can be populated differently.

Rotating potentials have Rotating potentials have Lagrange pointsLagrange points..

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