Notes The principle of least action The notion of least action is a key concept in the Hamiltonian formulation. This is a more general kind of path variation where time and coordinates for position are both ...
Notes Hamilton's equation of motion from variational principle Hamilton's principle is stated as:Equation 1 is sometimes referred as the modified Hamilton's principle. This principle leads Hamilton's cannonical equations of motion as shown belowLabelling each of …
Notes Euler's angles The orientation of a rigid body must be specified by three independent factors in order for the associated orthogonal transformation matrix to have the determinant +1 and to be used ...
Notes Force free motion of a symmetrical rigid body Let us choose the symmetry axis as the principle z axis, so that I1 = I2 and Euler's equations simplifies towhere A is some constant and we have chosen ...
Notes Condition for steady Precession of Heavy Symmetrical top with one point fixed Consider the motion of a heavy symmetrical top spinning about the axis of symmetry, viz z'axis. The top is subject to a gravitational torque and is locked at its lower ...
Notes Heavy symmetrical top with one point fixed We can select a particular set of body axes such that the off-diagonal elements vanish and the expression of inertia only contains the diagonal elements. These axes are known as ...
Notes Rigid bodies- Kinematics and Dynamics The independent coordinates of a rigid bodyConsider a rigid body with three non-collinear points p, q, and r. Since each particle has three degrees of freedom, a total of ...
Notes Type of the canonical transformation generated by W Consider a canonical transformation in which the new momenta pj are all constants of the motion α in particular is the constant of motion H, i.e., H(qj,pj)= α . Taking ...
