## CHASSIS - Inverse Modelling of Relaxed Dynamical Systems

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Chakrabarty, Dalia

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The state of a non-relativistic gravitational dynamical system is known at
any time $t$ if the dynamical rule, i.e. Newton's equations of motion, can be
solved; this requires specification of the gravitational potential. The
evolution of a bunch of phase space coordinates ${\bf w}$ is deterministic,
though generally non-linear. We discuss the novel Bayesian non-parametric
algorithm CHASSIS that gives phase space $pdf$ $f({\bf w})$ and potential
$\Phi({\bf x})$ of a relaxed gravitational system. CHASSIS is undemanding in
terms of input requirements in that it is viable given incomplete,
single-component velocity information of system members. Here ${\bf x}$ is the
3-D spatial coordinate and ${\bf w}={\bf x+v}$ where ${\bf v}$ is the 3-D
velocity vector. CHASSIS works with a 2-integral $f=f(E, L)$ where energy
$E=\Phi + v^2/2, \: v^2 = \sum_{i=1}^{3}{v_i^2}$ and the angular momentum is $L
= |{\bf r}\times{\bf v}|$, where ${\bf r}$ is the spherical spatial vector.
Also, we assume spherical symmetry. CHASSIS obtains the $f(\cdot)$ from which
the kinematic data is most likely to have been drawn, in the best choice for
$\Phi(\cdot)$, using an MCMC optimiser (Metropolis-Hastings). The likelihood
function ${\cal{L}}$ is defined in terms of the projections of $f(\cdot)$ into
the space of observables and the maximum in ${\cal{L}}$ is sought by the
optimiser.

Comment: 7 pages, 2 figures, 1 paged abstract - shorter version of the abstract presented here, accepted after review for publication in the proceedings of the 18th IMACS World Congress - MODSIM09 International Congress on Modelling and Simulation, Cairns, Australia, 2009

Comment: 7 pages, 2 figures, 1 paged abstract - shorter version of the abstract presented here, accepted after review for publication in the proceedings of the 18th IMACS World Congress - MODSIM09 International Congress on Modelling and Simulation, Cairns, Australia, 2009

##### Keywords

Mathematics - Statistics Theory, Astrophysics - Instrumentation and Methods for Astrophysics