Game Development Reference
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nators, thus dropping out of the equations. Recall that the weight of an object is its mass
times the acceleration due to gravity, g , which is 9.8 m/s 2 at sea level.
The formulas for calculating the total mass and center of gravity for a system of discrete
point masses can conveniently be written in vector notation as follows:
m t = Σ m i
CG =[Σ ( cg i ) (m i )] / m t
where m t is the total mass, m i is the mass of each point mass in the system, CG is the
combined center of gravity, and cg i is the location of the center of gravity of each point
mass in design, or reference, coordinates. Notice that CG and cg i are shown as vectors
since they denote position in Cartesian coordinates. This is a matter of convenience
since it allows you to take care of the x , y , and z components (or just x and y in two
dimensions) in one shot.
In the code samples that follow, let's assume that the point masses making up the body
are represented by an array of structures where each structure contains the point mass's
design coordinates and mass. The structure will also contain an element to hold the
coordinates of the point mass relative to the combined center of gravity of the rigid
body, which will be calculated later.
typedef struct _PointMass
float mass;
Vector designPosition;
Vector correctedPosition;
} PointMass;
// Assume that _NUMELEMENTS has been defined
Here's some code that illustrates how to calculate the total mass and combined center
of gravity of the elements:
int i;
float TotalMass;
Vector CombinedCG;
Vector FirstMoment;
TotalMass = 0;
for(i=0; i<_NUMELEMENTS; i++)
TotalMass FAC+= Elements[i].mass;
FirstMoment = Vector(0, 0, 0);
for(i=0; i<_NUMELEMENTS; i++)
FirstMoment += Element[i].mass * Element[i].designPosition;
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