Part II. Writing the equation d² [x = x − x², in the form of the system dx = = V, v=x-x² W(x) x = x(t), x= x(t), v = v(t), v² + W (x) = const for each solution (r(t), v(t)) to system (2), where the potential energy is given by the antiderivative of -x +x², x² = (a) Find all the stationary points (x, v) (the points where di = 0, d = 0). (b) Find the corresponding linear system near each critical point. (c) (d) Find the corresponding linear system near each critical point. Draw a phase portrait of the system near each critical point. Draw a phase portrait taking into account the energy conservation, (e) 2 + (1) co/8 (2)
Part II. Writing the equation d² [x = x − x², in the form of the system dx = = V, v=x-x² W(x) x = x(t), x= x(t), v = v(t), v² + W (x) = const for each solution (r(t), v(t)) to system (2), where the potential energy is given by the antiderivative of -x +x², x² = (a) Find all the stationary points (x, v) (the points where di = 0, d = 0). (b) Find the corresponding linear system near each critical point. (c) (d) Find the corresponding linear system near each critical point. Draw a phase portrait of the system near each critical point. Draw a phase portrait taking into account the energy conservation, (e) 2 + (1) co/8 (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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