Chapter 8

Show that if \(\lambda\), are the eigenvalues of a square matrix, then if the reciprocal matrix exists it has the eigenvalues \(\lambda_{i}^{-1}\)

A dynamical system has the Lagrangian $$L=\dot{q}_{1}^{2}+\frac{\dot{q}_{2}^{2}}{a+b q_{1}^{2}}+k_{1} q_{1}^{2}+k_{2} \dot{q}_{1} \dot{q}_{2}$$ where \(a, b, k_{1},\) and \(k_{2}\) are constants. Find the equations of notion in the Hamiltonian formulation.