uniker9/JAutoDiff @ GitHub

PlanarSolarSystemApplet

A demonstration of JAutoDiff (A pure Java automatic differentiation library).
This applet program shows a dynamics of Sun-Earth-Moon system defined as

(Eq. 1): x_sun = 0; x_earth = x_sun + a_earth (cos(θ_{0 earth} + w_earth(t - t₀)), sin(θ_{0 earth} + w_earth(t - t₀)))^T; x_moon = x_earth + a_moon (cos(θ_{0 moon} + w_moon(t - t₀)), sin(θ_{0 moon} + w_moon(t - t₀)))^T

where x denotes position of the astronomical objects.

Press the key 'v' on the applet, then you can see the dynamics in state spaces of velocity.
While only the above equations (Eq.1) are coded manually in this program,
JAutoDiff generates the derivative below (Eq.2) of (Eq.1) with respect to time t.

(Eq. 2): v_sun = 0; v_earth = v_sun + a_earthw_earth (-sin(θ_{0 earth} + w_earth(t - t₀)), cos(θ_{0 earth} + w_earth(t - t₀)))^T; v_moon = v_earth + a_moonw_moon (-sin(θ_{0 moon} + w_moon(t - t₀)), cos(θ_{0 moon} + w_moon(t - t₀)))^T

Actually, this program simulates the dynamics with initial condition such that
θ_{0 earth}=θ_{0 moon}=0 at an arbitrary time in the time interval t₀ = [-50000.0, 50000.0] ⊂ R.
The state variables x, v are computed as real interval vectors using interval arithmetics library ia_math.
The rectangles in the applet show bounds of the state variables.