If different coordinate systems are selected, the specific values of the centroid coordinates will be different, but the relative position of the centroid relative to each particle in the particle system has nothing to do with the selection of coordinate systems. The center of mass of a particle system is only related to the relative position of the mass and distribution of each particle.

Extended data:

Centroid analysis;

Let's assume a particle system consisting of n particles, and the mass of each particle is m 1, m2, …, mn. If you use r 1.

, r2, ..., rn respectively represent the vector diameter of each particle in the particle system relative to the fixed point rc.

The vector diameter representing the center of mass is RC = (m1r1+m2r2+...+mnrn)/(m1+m2+...+Mn).

When an object has a continuously distributed mass, the vector diameter RC of the center of mass C = ∫ ρ rd ρ/∫ρd ρ, where ρ is the density of the object (or surface or line); Dτ is a volume (or surface, line) element equivalent to ρ; Integral the whole material body (or surface or line) with the distribution density ρ. The motion theorem of the center of mass can be deduced from Newton's law of motion or momentum theorem of particle system.

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