Center of Mass  Matrix Representation

04052015, 04:05 AM
Post: #1




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 Code: EXPORT CENTERMTX(m) 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 

04052015, 10:29 PM
Post: #2




RE: Center of Mass  Matrix Representation
Congrats for your program, I´m going to download to my calculator. This is the first step for simebody who wants to program the famous and impressive "Sección" program for HP48 or 50, with gravity center, moments of inertia etc, on any shape, any.


04062015, 03:09 PM
Post: #3




RE: Center of Mass  Matrix Representation
(04052015 10:29 PM)akmon Wrote: Congrats for your program, I´m going to download to my calculator. This is the first step for simebody who wants to program the famous and impressive "Sección" program for HP48 or 50, with gravity center, moments of inertia etc, on any shape, any. I quote! thank you, Eddie Salvo ∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C  DM42 WP34s :: Prime Soft. Lib 

04072015, 06:33 AM
Post: #4




RE: Center of Mass  Matrix Representation
I´ve tried a little example to manage the program, but I didn´t get the results I expected. I want to know the center of gravity of a triangle. The coordinates are (0,0), (5,0) and (5,5). I suppose mass 1 for every points, so I write this matrix:
[[0 0 1][5 0 1][5 5 1]] The gravity center sould be (10/3 5/3), but I don´t get that result. What am I doing bad? Thank you. 

04082015, 05:48 PM
(This post was last modified: 04082015 05:51 PM by Thomas Ritschel.)
Post: #5




RE: Center of Mass  Matrix Representation
(04072015 06:33 AM)akmon Wrote: I´ve tried a little example to manage the program, but I didn´t get the results I expected. I want to know the center of gravity of a triangle. The coordinates are (0,0), (5,0) and (5,5). I suppose mass 1 for every points, so I write this matrix: Note that the matrix does not contain the coordinates and associated masses, but rather it's a grid representation of point masses. There is an explanation of the matrix in Eddie's blog. For your example the matrix may be entered as (6x6 matrix, e.g. 0 to 5 = 6 grid points): [[1 0 0 0 0 1][0 0 0 0 0 0][0 0 0 0 0 0][0 0 0 0 0 0][0 0 0 0 0 0][0 0 0 0 0 1]] This will yield the center of mass at grid position (13/3 8/3), having a (+1 +1) offset with respect to your solution (note that the origin (0 0) is at grid position (1 1)). 

04082015, 07:35 PM
Post: #6




RE: Center of Mass  Matrix Representation
The following program computes the center of mass for arbitrary arrangements of mass points in 3D cartesian space. For a system consisting of n particles the input is a nby4 matrix, e.g. the x, y, z coordinates in the the first three columns and the masses in the forth column.
Code: EXPORT CG(xyzm) Using akmon's example: Code: CG([[0 0 0 1][5 0 0 1][5 5 0 1]]) = [3.333333333 1.666666667 0] = [10/3 5/3 0] 

04092015, 10:48 AM
Post: #7




RE: Center of Mass  Matrix Representation
Thank you very much for your version, Thomas. That´s what I was searching, easier for matrix input, even I edited it simpler, because 99% I work in 2D only.


07032015, 03:40 PM
(This post was last modified: 07032015 03:50 PM by chromos.)
Post: #8




RE: Center of Mass  Matrix Representation
(04072015 06:33 AM)akmon Wrote: I´ve tried a little example to manage the program, but I didn´t get the results I expected. I want to know the center of gravity of a triangle. The coordinates are (0,0), (5,0) and (5,5). I suppose mass 1 for every points, so I write this matrix: There is builtin function in HP Prime for this. Geocaching Coords Solver, Number of triangles Puzzle 

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