Description 
NBODYVECT  Fully vectorized nbody equation
nbodyVect(x0,dx0,mus,t) integrates the nbody equations of motion using either a symplectic second order integrator, or any of the standard builtin or user supplied first order integrators.
x0  3n x 1 stacked initial position vectors:
[r1(1);r1(2);r1(3);r2(1);r2(2)r2(3);...;rn(1);rn(2);rn(3)]
dx0  3n x 1 stacked initial velocity vectors
mus  gravitational parameters (G*m_i) where G is the gravitational constant and m_i is the mass of the ith body.
t  time span: either a 2 element array of initial and final time, or array of all time steps to output.
All units must be complementary, i.e., if positions are in AUs, and time is in days, dx0 must be in AU/day and mus must be in AU^3/day^2 (these are the units in solarSystemData.mat). This data was downloaded from JPL's System Web Interface (http://ssd.jpl.nasa.gov/?horizons)
To switch to first order integrator, comment line 61, and uncomment lines 6465. Line 61 should be replaced with your symplectic integrator of choice, such as rkn86 (this needs modifications to accept arbitrary time arrays).
Example:
%integrate solar system for one year
ssdat = load('solarSystemData.mat');
[t,x,dx] = nbodyVect(ssdat.p0,ssdat.v0,ssdat.mus,0:1:365);
%plot first 3 orbits
plot3(x(:,1),x(:,2),x(:,3),x(:,4),x(:,5),x(:,6),x(:,7),...
x(:,8),x(:,9))
