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SUPPORT SITE |
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Path: Orbit/OrbitMechanics
% Dimensionalize or non-dimensionalize an orbit. dir determines the direction. dir = 0 or dir omitted will non-dimensionalizes r, v, t and mu. r, v and t may be vectors. We non-dimesionalize as follows: Quantity Units Nondimensionalizing Constanst r [L] rRef t [T] rRef/sqrt(mu/rRef) v [L/T] sqrt(mu/rRef) mu [L^3/T^2] mu accel [L/T^2] mu/rRef^2 sqrt(mu/r) = v = L/T so we pick T = rRef/sqrt(mu/r) Non-dimensional units are often better for estimation and optimization. For circular orbits the nominal orbit radius is best for rRef. For other orbits, such as a geosynchronous transfer orbit you can pick the mean orbit. When using nondimensional units you must non-dimensionalize the external accelerations by multiplying by fAcc. Type NonDimensionalOrbit for a simulation of a circular planar orbit at 1 AU from the sun. It will plot non-dimensional and dimensional units. In non-dimensional units r and v will oscillate between +/- 1. Since version 2014.1 -------------------------------------------------------------------------- Form: [r, v, t, mu, fAcc] = NonDimensionalOrbit( r, v, t, mu, rRef, dir ) -------------------------------------------------------------------------- ------ Inputs ------ r (3,:) Position vectors v (3,:) Velocity vectors t (1,:) Time vector mu (1,1) Gravitational constant rRef (1,1) Reference length dir (1,1) 0 or no input means non-dimensionalize ------- Outputs ------- r (3,:) Position vectors v (3,:) Velocity vectors t (1,:) Time vector mu (1,1) Gravitational constant fAcc (1,1) Acceleration scaling --------------------------------------------------------------------------
Common: Database/Constant Common: Graphics/Plot2D Common: Graphics/TimeLabl Math: Integration/RK4 SC: BasicOrbit/Period SC: BasicOrbit/RHSOrbit
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