Leibniz's Contributions to Mechanics
3
To start off we need to first tackle continuity. Leibniz was adamant about the fact that "nature does nothing in leaps" (2). Continuity is of course the foundation of differential calculus. This naturally leads into the calculus. Leibniz independent of Isaac Newton developed Differential and Integral calculus. The Leibniz notation was easier to follow and learn than Newtonian Notation in the sense that it's useable to me.
He invented the differential notation we use today
which is includes much more information than the newtonian overdot notation
which looks like this
(2). As well as the integral sign currently used
(2).This of course led to his dispute with Newton for the latter part of his
life. His other big contribution to mechanics was his study of the differential
equations. Leibniz is responsible for the mothod of seperation of variables
which is the decomposition of a partial differential equation into two or
more ordinary differential equations which can be solved linearly from there.
Differential equations (esspecially partial differential equations) are the
basis for most of mechanics this is kind of a big deal (2). The final main
contribution to mechanics for which Leibniz is responsible is the conservation
of kinetic energy. Leibniz believed quite strongly in the "vis viva"
which translates to the living force (2). It became a major point of contention
between Leibniz and Cartesians who preferred the term mass times velocity
which we now called momentum since it was conserved in inelastic collisions
as well. It was another one hundred and fifty years before conservation laws
again came to the forefront of physics (2).Leibniz tackeled several other
topics in mathematics. He was the first to express numbers in binary and was
a huge proponent of it. Leibniz believed that binary was the mathematics of
god with 1 representing god and zero representing void (5). He also invented
the first mechanical step wheeled calculator which expressed answers in decimal
form.