Physical Models

The physical modeling functionality is provided by DiffEqPhysics.jl and helps the user build and solve the differential equation based physical models.

Hamiltonian Problems

ODEs defined by Hamiltonians is described in the Dynamical ODEs section.

N-Body Problems

nprob = NBodyProblem(f, mass, vel, pos, tspan)

where f is the potential function, mass is the mass matrix, pos and vel are ArrayPartitions for the intial positions and velocity, and tspan is the timespan to solve on.

Example

In this example we will model the outer solar system planets.

G = 2.95912208286e-4
M = [1.00000597682, 0.000954786104043, 0.000285583733151, 0.0000437273164546, 0.0000517759138449, 1/1.3e8]
invM = inv.(M)
planets = ["Sun", "Jupiter", "Saturn", "Uranus", "Neptune", "Pluto"]

pos_x = [0.0,-3.5023653,9.0755314,8.3101420,11.4707666,-15.5387357]
pos_y = [0.0,-3.8169847,-3.0458353,-16.2901086,-25.7294829,-25.2225594]
pos_z = [0.0,-1.5507963,-1.6483708,-7.2521278,-10.8169456,-3.1902382]
pos = ArrayPartition(pos_x,pos_y,pos_z)

vel_x = [0.0,0.00565429,0.00168318,0.00354178,0.00288930,0.00276725]
vel_y = [0.0,-0.00412490,0.00483525,0.00137102,0.00114527,-0.00170702]
vel_z = [0.0,-0.00190589,0.00192462,0.00055029,0.00039677,-0.00136504]
vel = ArrayPartition(vel_x,vel_y,vel_z)

tspan = (0.,200_000)

const ∑ = sum
const N = 6
potential(p, t, x, y, z, M) = -G*∑(i->∑(j->(M[i]*M[j])/sqrt((x[i]-x[j])^2 + (y[i]-y[j])^2 + (z[i]-z[j])^2), 1:i-1), 2:N)
nprob = NBodyProblem(potential, M, vel, pos, tspan)
sol = solve(nprob,Yoshida6(), dt=100)