equation to maintain equilibrium?

Question

how do i write the equation to maintain equilibrium with forces

Answer 1

The simple answer is that the vector sum of the forces acting on an object must be zero if the object is to remain in "equilibrium" or in other words to have constant velocity.

Answer 2

When all the forces acting on an object is 0. The object has to be in a state where it cannot or does not apply an external force to it's state. The above definition is inclusive of motion and acceleration and momentum and so on. To increse or decrease it's equilbrium it has to be made to do it by applying an external force to it's state.

For example, in an accelerating equilibrium, the object has to an apply external force such as a friction to decrese it's accleration and therefore break free of it's state of equilibrium.

Answer 3

To be more complete, the vector sum in all coordinate directions (x,y,z) must sum to zero. as must the vector moments (torque). The linear sum prevents translation, the moment sum prevents rotation.