Take the spatial rectangular coordinate system Oxyz fixedly attached to the object, and use the coordinates xC, y C and zC to indicate the position of the center of gravity C of the object, as shown in Figure 6-25. The gravitational force on each small piece of an object is expressed by δ P 1, δ P2, ..., and it is considered that they form a spatial parallel force system. The resultant force of this parallel force system is the weight of the object:

p =σδ？ p？ Me?

The line of action of the resultant force passes through the center of gravity C(xC, y C, zC) of the object. According to the resultant moment theorem, there are

Px？ c？ =ΣΔ? p？ Me? x？ Me?

So there is

x？ c？ =? ΣΔ? p？ Me? x？ Me? p？

Similarly, available

y？ c？ =? ΣΔ? p？ Me? y？ Me? p？

In order to determine another coordinate zC of the object's center of gravity, the coordinate system and the object rotate 90 degrees around the Y axis, so that the X axis is vertical and the direction of gravity is parallel to the X axis ... By applying the resultant moment theorem, we can get

z？ c？ =? ΣΔ? p？ Me? z？ Me? p？

So the general formula for obtaining the coordinates of the center of gravity is

x？ c？ =? ΣΔ? p？ Me? x？ Me? p？ ,? y？ c？ =? ΣΔ? p？ Me? y？ Me? p？ ,? z？ c？ =? ΣΔ? p？ Me? z？ Me? P