Editing D'Alembert's principle (section)

==Dynamic equilibrium==
D'Alembert's form of the principle of virtual work states that a system of rigid bodies is in dynamic equilibrium when the virtual work of the sum of the applied forces and the inertial forces is zero for any virtual displacement of the system.  Thus, dynamic equilibrium of a system of <math>n</math> rigid bodies with <math>m</math> generalized coordinates requires
<math display="block"> \delta W = \left(Q_1 + Q_1^*\right) \delta q_1 + \dots + \left(Q_m + Q_m^*\right) \delta q_m = 0,</math>
for any set of virtual displacements <math>\delta q_j</math> with <math>Q_j</math> being a [[Generalized forces#D'Alembert's principle|generalized applied force]] and  <math>Q^*_j</math> being a generalized inertia force.  This condition yields <math>m</math> equations,
<math display="block"> Q_j + Q^*_j = 0, \quad j=1, \ldots, m,</math> 
which can also be written as
<math display="block"> \frac{d}{dt} \frac{\partial T}{\partial \dot{q}_j} -\frac{\partial T}{\partial q_j} = Q_j, \quad j=1,\ldots,m.</math>
The result is a set of m equations of motion that define the dynamics of the rigid body system.