Center of Mass - Matrix Representation

[Eddie W. Shore]

The HP Prime program CENTERMTX calculates the center of mass of the matrix M, where M represents the body. The entries of M represents an array of molecules, each with assigned weights. It is possible that the center of mass is located outside of the body.

Note: If gravity affects the particles equally, then the center of mass & center of gravity are identical.

Formulas:

Xc = ∑(x * m)/∑m
Yc = ∑(y * m)/∑m


HP Prime: CENTERMTX

Code:

EXPORT CENTERMTX(m)
BEGIN
// Center of Mass: matrix
// Matrix of mass
LOCAL s,tm,rt,ct,r,c;
// in MAKEMAT I=row,J=col
s:=SIZE(m);
r:=s(1);
c:=s(2);
// Total Mass
tm:=TRN(m*MAKEMAT(1,c,1))*
MAKEMAT(1,r,1);
tm:=tm(1,1);
// Row Total
rt:=TRN(m*MAKEMAT(I,c,1))*
MAKEMAT(1,r,1);
rt:=rt(1,1);
// Column Total
ct:=TRN(TRN(m)*MAKEMAT(I,r,1))*
MAKEMAT(1,c,1);
ct:=ct(1,1);
// center
RETURN [[rt/tm,ct/tm]];
END;

Example: Locate the center of mass of the following body.

M = [[1 , 2, 1], [1, 1, 2],[1, 2, 1]]

The center of mass: [[ 2.08333333333, 2 ]]

http://edspi31415.blogspot.com/2015/04/h...atrix.html