Leibniz's Contributions to Mechanics

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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.