Solving the Collisionless Boltzmann Equation
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چکیده
Equilibrium stellar-dynamical systems are described by the time-independent Collisionless Boltzmann Equation (CBE). Two methods of building equilibrium stellar-dynamical systems are described. One begins by defining integrals of motion I1, I2, . . .; Jeans theorem implies that any function F = F(I1, I2, ...), is a solution of the time-independent CBE. Another begins by defining the mass distribution of the desired model; Schwarzschild’s method then tries to find a set of orbits which, when superimposed, reproduce that mass distribution. Non-equilibrium stellar-dynamical systems are described by the time-dependent CBE. This equation can be effectively solved with a Monte-Carlo technique which represents the distribution function f (r,v,t) as a set of N bodies.
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