%partic2.m - given the mass and initial positions, velocities, and
%accelerations of 3 particles, this script calculates their linear
%and angular momenta, energies, forces, and torques
%help symbolic %type this if need help on symbolic functions
clear;
format compact; %Suppress extra line-feeds on outputs
u=[1,1,1]; %vector used for component sum
m=[1,2,3]; %mass vector
M=sum(m); %total mass
r =[5,4,0;-1,2,0;1,-3,0]; %position vectors
v =[4,0,0;-1,2,0;0,-6,0]; %velocity vectors
a =[4,0,0;2,0,0;0,-6,0]; %acceleration vectors
rcm =[1.0,-0.1667,0]; %center of mass position vector
vcm =[0.3333,-2.3333,0]; %center of mass velocity vector
acm =[1.3333,-3.0000,0]; %center of mass acceleration vector
for i=1:3
p(i,:)=m(i)*v(i,:); %momentum calculation
l(i,:)=cross(r(i,:),p(i,:)); %angular momentum calculation
e(i)=dot(p(i,:),p(i,:))/2/m(i); %kinetic energies
f(i,:)=m(i)*a(i,:); %forces
tau(i,:)=cross(r(i,:),f(i,:)); %torques
end
p %obtained momenta
P=u*p %net momentum 1st way
P=M*vcm %P center of mass way
l %obtained angular momenta
L=u*l %net angular momentum
e %energies
E=sum(e(:)) %total kinetic energy
f %obtained forces
F=u*f %net force 1st way
F=M*acm %F center of mass way
tau %obtained torques
Tau=u*tau %Net torque