Example: Euler's Equations
Euler's equations provide an excellent illustration of Appell's formulation.
Consider a rigid body of N particles joined by rigid rods. The rotation of the body may be described by an angular velocity vector, and the corresponding angular acceleration vector
The generalized force for a rotation is the torque N, since the work done for an infinitesimal rotation is . The velocity of the kth particle is given by
where rk is the particle's position in Cartesian coordinates; its corresponding acceleration is
Therefore, the function S may be written as
Setting the derivative of S with respect to equal to the torque yields Euler's equations
Read more about this topic: Appell's Equation Of Motion