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The concept of adding air drag to motion equations, which cannot be solved analytically. Students will learn how to use euler's method to find approximate solutions. The equations for a falling ball with air drag, the review of the euler process, and the trajectory of a projectile with air drag. The document also discusses the convergence of euler's method.
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ME123 Computer Applications I
ME123 Computer Applications I
Suppose we have a ball falling: ๐๐ ๐ ๐๐ ๐๐ก = โ๐๐ + ๐๐^2 ๐๐ ๐๐ก = โ๐ + ๐ ๐ ๐^2 This one is much harder to solve analytically. ๐๐^2
๐๐ ๐๐ ๐๐ก = โ๐ + ๐ ๐ ๐^2 ๐ 0 = 0 You will work with these equations in the exercises. ๐๐ฆ ๐๐ก = ๐ ๐ฆ 0 = 0 ๐๐^2 This is the only new term!
ME123 Computer Applications I
ME123 Computer Applications I
Launch a projectile with air drag: This one has NO exact solution. It MUST be solved numerically. ๐๐ ๐๐^2 The air drag always acts to oppose the motion of the projectile. Its magnitude depends on the square of the magnitude of the velocity.
Launch a projectile with air drag: ๐๐ ๐ ๐๐๐ฅ ๐๐ก = โ๐ ๐๐ฅ ๐ ๐^2 ๐๐ฅ 0 = ๐๐๐๐ข๐๐โ cos ๐ ๐๐ฅ ๐๐ก = ๐๐ฅ ๐ฅ 0 = 0 ๐๐^2 x y ๐ ๐๐๐ฆ ๐๐ก = โ๐ ๐๐ฆ ๐ ๐^2 โ ๐๐ ๐๐ฆ 0 = ๐๐๐๐ข๐๐โ sin ๐ ๐๐ฆ ๐๐ก = ๐๐ฆ ๐ฆ 0 = 0 You will work with these equations in the Exercises.
