Part II. Writing the equation d² ; =r_r dt2x in the form of the system v² d dt x = v, v=x-x² W(x): = x(t), x = x = = x(t), v = v(t), == (a) Find all the stationary points (x, v) (the points where d = 0, dt = 0). dt (b) Find the corresponding linear system near each critical point. (c) Find the corresponding linear system near each critical point. (d) Draw a phase portrait of the system near each critical point. (e) Draw a phase portrait taking into account the energy conservation, 1 +W(x) = const for each solution (x(t), v(t)) to system (2), 2 where the potential energy is given by the antiderivative of -x +x², x² x³ + 2 3 (1) (2)
Part II. Writing the equation d² ; =r_r dt2x in the form of the system v² d dt x = v, v=x-x² W(x): = x(t), x = x = = x(t), v = v(t), == (a) Find all the stationary points (x, v) (the points where d = 0, dt = 0). dt (b) Find the corresponding linear system near each critical point. (c) Find the corresponding linear system near each critical point. (d) Draw a phase portrait of the system near each critical point. (e) Draw a phase portrait taking into account the energy conservation, 1 +W(x) = const for each solution (x(t), v(t)) to system (2), 2 where the potential energy is given by the antiderivative of -x +x², x² x³ + 2 3 (1) (2)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.7: Solving Systems Of Linear And Quadratic Equations
Problem 3GP
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