14. Reconsider the space docking problem of Example 5.2, but now approxi- mate the discrete time dynamical system Да1 — — kwr1 — кс^2 Δυ = x1 – X2 by its continuous time analogue dx1 -kwx1 kcx2 dt dx2 = x1 – x2 dt (a) Show that the continuous time model has a stable equilibrium at (0,0). Assume w = 10, c = 5, and k 0.02. (b) Solve the continuous model, using the method of eigenvalues and eigenvectors.

14. Reconsider the space docking problem of Example 5.2, but now approxi- mate the discrete time dynamical system Да1 — — kwr1 — кс^2 Δυ = x1 – X2 by its continuous time analogue dx1 -kwx1 kcx2 dt dx2 = x1 – x2 dt (a) Show that the continuous time model has a stable equilibrium at (0,0). Assume w = 10, c = 5, and k 0.02. (b) Solve the continuous model, using the method of eigenvalues and eigenvectors.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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