How is Mass distribution done?

How is Mass distribution done?

Anonymous (65.120.67.x) 14 Apr 2008 16:06

In physics, weight distribution effects how an object moves and collides with other objects. Here is the code I'm looking at to set Mass for the carObject.

body.Mass = mass;
Vector3 min, max;
car.Chassis.GetDims(out min, out max);
Vector3 sides = max - min;

float Ixx = (1.0f / 12.0f) * mass * (sides.Y * sides.Y + sides.Z * sides.Z);
float Iyy = (1.0f / 12.0f) * mass * (sides.X * sides.X + sides.Z * sides.Z);
float Izz = (1.0f / 12.0f) * mass * (sides.X * sides.X + sides.Y * sides.Y);

Matrix inertia = Matrix.Identity;
inertia.M11 = Ixx; inertia.M22 = Iyy; inertia.M33 = Izz;

If the bounds of the car is (4,2,2) and the Mass given is 100 the Ixx value is 66.66…, and the Iyy/Izz values are 166.66… Which make no sense to me at all. Shouldn't these values equal 100 when added up? I also don't get the arbitrary divide by 12.

Re: How is Mass distribution done?

jwatte 14 Apr 2008 19:05

That is because the inertia tensor is calculated as a 3D matrix.

The division by 12 is because that's how the mass distribution for a box is derived analytically (similar to how the volume of a sphere is radius cubed times 4/3 pi).

I believe that the eigenvalue of that inertia tensor will be the mass value 100 IIRC. The reason the different axes have different sums is that the distribution of mass isnt' even in a box. Try creating the inertia tensor for a sphere of mass 100 and compare, if you don't believe me :-)

Re: How is Mass distribution done?

protomor 14 Apr 2008 19:40

I always forget to sign in >_<

Ok, so what is the best way to edit these values to give my car object different weight distribution? I mainly want to be able to control the height and front to back weight distribution. The car currently reacts much like an SUV. I'm hoping lowering the center of gravity will help to alleviate the issue.