Guide Analytical Mechanics for Engineers

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This work, dubbed "the theory of impetus," would undergo major revisions in the sixth, 12th and 14th centuries A. Terrestrial mechanics thusly became the study of how things move and interact on the Earth's surface. By the 16th century, scholars began to notice that the theory of impetus was ill suited for describing many phenomena — in particular, projectiles flung from catapults and cannons. According to the theory, a projectile should fly through the air until it runs out of impetus, whereupon it should fall straight to the ground.

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In reality, the path of a projectile is a very specific curve. To make sense of these observations, according to Bernard Cohen in " The Birth of a New Physics " Norton, , scientists began to think about gravity pulling on objects with uniform acceleration. In his publication, " Dialogues Concerning Two New Sciences ," Galileo Galilei published the first mathematical proof that uniform acceleration would cause projectiles to move in parabolic trajectories that matched observations, thus showing that terrestrial mechanics are governed by mathematics. Similarly, and also in the 16th century, celestial mechanics was shown to have extremely strong ties to mathematics.

According to David S. Johannes Kepler based his three laws of planetary motion, on Brahe's data for the motion of Mars. The first of these laws, published in his work, " Astronomia Nova ," showed that planets move in elliptical paths around the sun. Seventy years later, Newton built on the work of Galileo and Kepler to show that the elliptical movements of the celestial realm and parabolic movements of the terrestrial realm could be explained by one elegant mathematical law, his Law of Universal Gravitation.

In addition, he formalized the laws of motion by describing them in the language of mathematics. Using Newton's laws, scientists could manipulate symbolic math with algebra and calculus also co-invented by Newton to learn about phenomena not yet observed. Classical mechanics grew throughout the 18th and 19th centuries to describe everything from optics, fluids and heat to pressure, electricity and magnetism.

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