Math/Engineering help needed....

I'm working on a project for school, and I'm having a hard time trying
to figure it out. What is required is to write a program, of our
choice, to find the section properties of an arbitrary shaped region
from coordinates of its vertices.

Section Properties include:
1. Area
2. Centroid location
3. Moments of Inertia


The Area and Centroid Locations are straight forward, but I've been
having problems determining the Moments of Inertia. If anyone can
help me out it would be greatly appreciated. Remember, all I know is
the coordinates of the vertices, and it's an arbitrary cross-section.

email me at

Thanks,
-Matt

 

Required Reading for Mathematicians


The Jacobins and their struggle for Independence
A 10 day diet to improve indeterminate forms
Cheaper by the Googol
1001 best loved double integrals
The Torus and I
A short table of even primes (abridged)
Will success spoil Runge-Kutta?
Dining out on Hilbert space
100 tasty fillings for empty sets
How to keep condensation points from dripping into open sets
A child's garden of Chebyshev polynomials
Tom Swift and his electronic cycloid
A treasury of matrices - upright and inverted
Improving Lipschitz conditions in the slums
How to prevent rust on Riemann surfaces
The decline and fall of exp(-x)
First aid for Dedekind cuts and bruises
The Peano postulates transcribed for violin and cello
A collection of happy endings for incomplete Beta functions
Lebesque integration in the United States
One million random digits in ascending order

 

Get thee a copy of Machinery's Handbook. All of this information is there.

Also try efunda.com.

(-Matt) wrote in message

 

see http://www.efunda.com/math/areas/Common_Geometric_Shapes_Index.cfm
and http://em-ntserver.unl.edu/NEGAHBAN/EM223/note18/note18.htm

Assuming it's a 2D section n-sided shape your dealing with...

The shape can be parsed into a set of triangles and various 4-sided
figures. For each of the figures, compute the area, centroid, and
moment of inertia. Consult one of your textbooks for the methods to
combine moments of interita and centroids of the pieces.

For centroids, it's the average of the (x,y) coordinates weighted
w.r.t. the area of each section.

For inertia about an axis, multiply the inertia about the centroid
times the square of the distance to the axis for each section.