Equilibrium

AKA statics stuff

Either has zero velocity or constant velocity. Determined by two main equations: $\Sigma F=0$ $\Sigma M=0$ Basically solve taking moments about optimal points, and summing forces along an axis to form systems of equations. Then use those systems of equations to solve.

In rigid body problems, moments and forces on each of the 3D axis (6 total) are required to express equilibrium conditions.

See lecture 1

Solving 3D Equilibrium Equations

Not hard but tedious.

1. Find forces in their vector form: $\overrightarrow{T_{AB}}=\frac{\overrightarrow{r_B}-\overrightarrow{r_A}}{|r_B+r_A|}$
2. You will have equations with i, j, and k components.
3. Then write equilibrium equations in the i, j, and k directions and set each to 0! This yields 3 equations.
4. For more equations, take moment about the most populated points (in 3D use the cross product) to get a another equation that you can use to solve to find your unknown forces. $\Sigma M_{direction}=0$
   $\Sigma M_x=T_{ab}\times r_{ab}+\cdots$
   Basically, things along the axis of the point of which you take a moment of are ignored in summing moments, but you need to consider all other forces and take the cross product of the force, with its position vector to the point at which the moment is being taken.
   

Solve the system of equations using su. , matrices, etc.