HP Prime: Center of Mass - Matrix Representation

HP Prime:  Center of Mass - Matrix Representation

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

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.

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

Eddie

This blog is property of Edward Shore.  2015.