Computer Algebra Recipes for Mathematical Physics by Richard H. Enns

By Richard H. Enns

* makes use of a pedagogical technique that makes a mathematically not easy topic more uncomplicated and extra enjoyable to learn

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I. M. Curious who will discuss in her own words the elegant and thorough computer algebra solution that she generated in solving the following problem involving a familiar nonhomogeneous LODE. A mechanical system (of unit mass) experiences a Stokes’s law drag force FStokes = −2 α x, ˙ a Hooke’s law restoring force FHooke = −ω 2 x, and a driving force FDrive = f cos(Ω t + δ). Here α is a positive constant, ω the natural frequency, f the force amplitude, Ω the driving frequency, and δ a phase angle.

6: Resonance curves for f = 1 (bottom curve) to f = 5 (top). 6 Mr. Dirac’s Famous Function The man with a new idea is a crank until the idea succeeds. Mark Twain, Following the Equator, ch. 32, (1897). Consider a very long uniform horizontal beam glued to an elastic foundation, the foundation exerting a Hooke’s law restoring force. 3) YI dx4 where Y is Young’s modulus, I the moment of inertia of the beam’s crosssection about a horizontal axis, K the spring constant, and δ(x) the Dirac delta function.

Sol1:=dsolve({ode1,v(0)=0},v(t)); ode1 := gt sol1 := v(t) = V1 − e(− V1 ) V1 To compare with the experimental data, we need to calculate the distance that the bird falls in T seconds. For the Stokes model, this distance y1 is obtained by integrating the right-hand side (rhs) of sol1 from t = 0 to T . T); gT V1 (−V1 + g T + V1 e(− V1 ) ) y1 := g Let’s now look at Newton’s model of air resistance. Since the motion is in one direction (down) only, the absolute value sign can be dropped, so that FNewton = −b m v 2 .

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