Christiaan Huygens coined the term "centrifugal force" in his 1659 De Vi Centrifuga[2] and wrote of it in his 1673 Horologium Oscillatorium on pendulums.
In 1676–77, Isaac Newton combined Kepler's laws of planetary motion with Huygens' ideas, refined them, and foundthe proposition that by a centrifugal force reciprocally as the square of the distance a planet must revolve in an ellipsis about the center of the force placed in the lower umbilicus of the ellipsis, and with a radius drawn to that center, describe areas proportional to the times.
[3]Newton coined the term "centripetal force" (vis centripeta) in his discussions of gravity in his De motu corporum in gyrum, a 1684 manuscript which he sent to Edmond Halley.
An inverse cube law centrifugal force appears in an equation representing planetary orbits, including non-circular ones, as Leibniz described in his 1689 Tentamen de motuum coelestium causis.
[8] Later, Newton in his Principia crucially limited the description of the dynamics of planetary motion to a frame of reference in which the point of attraction is fixed.
Even the most ardent modern defenders of the cogency of Leibniz's ideas acknowledge that his harmonic vortex as the basis of centrifugal force was dynamically superfluous.
Later in the 18th century Joseph Louis Lagrange in his Mécanique Analytique explicitly stated that the centrifugal force depends on the rotation of a system of perpendicular axes.
Of course, addition of a speck of matter just to establish a reference frame cannot cause the sudden appearance of centrifugal force, so it must be due to rotation relative to the entire mass of the universe.
[18] The modern view is that centrifugal force is indeed an indicator of rotation, but relative to those frames of reference that exhibit the simplest laws of physics.
[22] By the end of the nineteenth century, some physicists had concluded that the concept of absolute space is not really needed...they used the law of inertia to define the entire class of inertial frames.
Purged of the concept of absolute space, Newton's laws do single out the class of inertial frames of reference, but assert their complete equality for the description of all mechanical phenomena.
Einstein succeeded, through many clever thought experiments, in showing that these apparently odd ramifications in fact had very natural explanation upon looking at just how measurements and clocks actually were used.
[7][8][30] Leibniz introduced the notions of vis viva (kinetic energy)[31] and action,[32] which eventually found full expression in the Lagrangian formulation of mechanics.