  We investigate regular and chaotic dynamics of Two Bodies Swinging on a Rod,
which differs from all the other mechanical analogies: depending on initial
conditions, its oscillation could end very quickly and the reason is not a drag
force or energy loss. We use various tools to analyze motion, such as
Poincar\'e section for quasi-periodic and chaotic cases. We calculate Lyapunov
characteristic exponent by different methods including Finite Time Lyapunov
Exponent analysis. Our calculations show that the maximal Lyapunov exponent is
always positive except in the marginal cases when one observes quasi-periodic
oscillations.
