physically consistent dynamical parameters subspaces

1d_physconst.m

N_PARTICLE = 4
N_SIMULATIONS = 100000

zeroth_moment = zeros(N_SIMULATIONS,1);
first_moment = zeros(N_SIMULATIONS,1);
second_moment = zeros(N_SIMULATIONS,1);

for i = 1:N_SIMULATIONS
  m = 100*rand(N_PARTICLE,1);
  x = 4*rand(N_PARTICLE,1)-2; %between -2 and 2 to have both 
  x2 = x.*x;
  x0 = x.**0;
  zeroth_moment(i) = dot(m,x0);
  first_moment(i) = dot(m,x); 
  second_moment(i) = dot(m,x2);
endfor

2d_physconst.m

da

3d_physconst.m

N_PARTICLE = 4
N_SIMULATIONS = 10000
N_DIM = 2
POS_RANGE = 2 
MASS_RANGE = 100

zeroth_moment = zeros(N_SIMULATIONS,1);
first_moment = zeros(N_SIMULATIONS,N_DIM);
second_moment = zeros(N_DIM,N_DIM,N_SIMULATIONS);

Ixx = zeros(N_SIMULATIONS,1);
Iyy = zeros(N_SIMULATIONS,1);
Ixy = zeros(N_SIMULATIONS,1);
 
for i = 1:N_SIMULATIONS
  m = MASS_RANGE*rand(N_PARTICLE,1);
  x = (2*rand(N_PARTICLE,N_DIM)-1)*POS_RANGE; %between -POS_RANGE and POS_RANGE to have both 
  second_moment_particle = zeros(N_PARTICLE,N_DIM,N_DIM);
  zeroth_moment(i) = sum(m);
  first_moment(i,:) = transpose(transpose(x)*m);
  for part = 1:N_PARTICLE
      second_moment(:,:,i) = second_moment(:,:,i) + m(part).*transpose(x(part,:))*x(part,:);
  endfor
endfor

for i = 1:N_SIMULATIONS
    Ixx(i) = second_moment(1,1,i);
    Iyy(i) = second_moment(2,2,i);
    Ixy(i) = second_moment(1,2,i);
endfor