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Student[Precalculus]

 CenterOfMass
 find the center of mass of a set of points

 Calling Sequence CenterOfMass(p1, ...)

Parameters

 p1, ... - each is an n-element list or Vector specifying a point, or a list whose first element is an n-element list or Vector and whose second element is an algebraic expression specifying the corresponding weight

Description

 • The command CenterOfMass(p1,p2,...,pn) computes the center of mass of the given points, weighted by the corresponding weights.  If a point is given as an n-element list or vector, the corresponding weight is taken to be 1.
 • All arguments must specify points of the same dimensionality (and orientation, when more than one of the points is a Vector).

Examples

 > $\mathrm{with}\left(\mathrm{Student}:-\mathrm{Precalculus}\right):$
 > $\mathrm{CenterOfMass}\left(\left[0,0\right],\left[1,1\right]\right)$
 $\left[\frac{{1}}{{2}}{,}\frac{{1}}{{2}}\right]$ (1)
 > $\mathrm{CenterOfMass}\left(\left[\left[0,1,2\right],0.1\right],⟨1,2,3⟩,\left[⟨-1,3,0⟩,0.5\right]\right)$
 $\left[{0.3125000000}{,}{2.250000000}{,}{2.000000000}\right]$ (2)
 > $\mathrm{CenterOfMass}\left(\left[⟨\mathrm{a1},\mathrm{b1}⟩,\frac{1}{3}\right],\left[⟨\mathrm{a2},\mathrm{b2}⟩,\frac{2}{3}\right]\right)$
 $\left[\begin{array}{c}\frac{{\mathrm{a1}}}{{3}}{+}\frac{{2}{}{\mathrm{a2}}}{{3}}\\ \frac{{\mathrm{b1}}}{{3}}{+}\frac{{2}{}{\mathrm{b2}}}{{3}}\end{array}\right]$ (3)