Celestial Mechanics Problem Set 2: The State Transition Matrix and Method of Differential Corrections
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چکیده
In this set of notes the State Transition Matrix for the N -body problem is developed. This matrix is the derivative of the flow generated by the N -body vector field with respect to initial conditions. It, and it’s inverse can be used in concert with the Newton Method in order to find/design orbits which begin at specified states and end in some specific configuration, such as a periodic orbit. We develop the differential equation which the State Transition Matrix satisfies, as well as the numerical methods necessary to solve it. The practical application of the matrix is discussed at length, especially it’s connection with
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تاریخ انتشار 2006