M(du)/(dt) = -γ u √(u^2 + v^2), m(dv)/(dt) = -γ v √(u^2 +...

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Texts: Nondimensionalize the system, where u_in ≈ 40 m/s; m ≈ 150 g is the mass of the baseball; u and v are, respectively, the horizontal and vertical components of the velocity of the baseball; t is the time since the release of the baseball by the pitcher; γ ≈ 0.01 g/cm is the friction constant of the baseball; g = 9.8 m/s^2 is the gravitational constant giving rise to a gravitational force mg downward on the baseball. And given that the drag force and gravitational force only slightly affect the ball’s motion and the magnitude of the frictional drag force is roughly comparable (but not exactly equal) to that of the gravitational force on a pitched baseball, what would you take as the small parameter in the perturbation theory? Under what conditions would you expect the perturbation theory to be accurate? du/dt = -yuV_u^2 + v^2 dv/dt = u(t=0) = u_in, v(t=0) = 0.

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$m\frac{du}{dt} = -\gamma u \sqrt{u^2 + v^2}$, $m\frac{dv}{dt} = -\gamma v \sqrt{u^2 + v^2} - mg$, $u(t = 0) = u_{in}$, $v(t = 0) = 0$.

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$m\frac{du}{dt} = -\gamma u \sqrt{u^2 + v^2}$, $m\frac{dv}{dt} = -\gamma v \sqrt{u^2 + v^2} - mg$, $u(t = 0) = u_{in}$, $v(t = 0) = 0$.

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