The Pendulum: from constrained fall to the concept of potential

History of Classical Mechanics from Galileo's free fall to the D.Bernoulli's first definition of potential. Presentation of D.Bernoulli's demonstration in Feynman's Lectures on Physics. Kuhn underlined the relevance of Galileo’s gestalt switch in the interpretation of a swinging body: from constrained fall to time metre. But the new interpretation did not eliminate the older one. The constrained fall, both in the motion of pendulums and along inclined planes, led Galileo to the law of free fall. Experimenting with physical pendulums and
assuming the impossibility of perpetual motion Huygens obtained a law of conservation of vis
viva at specific positions, beautifully commented by Mach. Daniel Bernoulli generalised
Huygens results introducing the concept of potential and the related independence of the
‘work’ done from the trajectories (paths) followed: vis viva conservation at specific positions is
now linked with the potential. Feynman’s modern way of teaching the subject shows striking
similarities with Bernoulli’s approach. A number of animations and simulations can help to
visualise and teach some of the pendulum’s interpretations related to what we now see as
instances of energy conservation.