Statics/Three-Dimensional Equilibrium

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There are six equations expressing the equilibrium of a rigid body in 3 dimensions.

Sum of Forces: \sum_{}^{} F_x=0, \sum_{}^{} F_y=0, \sum_{}^{} F_z=0

Sum of Moments: \sum_{}^{} M_x=0, \sum_{}^{} M_y=0, \sum_{}^{} M_z=0

To solve three dimensional statics problems:

  • Resolve force components
  • Resolve moments about a point
  • Resolve moments about a line or axis. See Scalar Triple Product

Knowing how to find the Determinate of a matrix can help alot here.