Applications.
In this problem, we indicate how to show that the trajectories are ellipses when the eigenvalues are purely imaginary.
Consider the system
(a) Show that the eigenvalues of the coefficient matrix are purely imaginary if and only if
(b) The trajectories of the system (i) can be found by convertingEqs. (i) into the single equation
Use the first of Eqs. (ii) to show that Eq. (iii) is exact.
(c) By
Where
Hint: What is the discriminant of the quadratic form in Eq. (iv) ?
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Differential Equations: An Introduction to Modern Methods and Applications
Additional Math Textbook Solutions
The Heart of Mathematics: An Invitation to Effective Thinking
Calculus Volume 1
Mathematics All Around (6th Edition)
Mathematical Ideas (13th Edition) - Standalone book
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning