Exploring Mae5790 7 Conservative Systems
Let's dive into the details surrounding Mae5790 7 Conservative Systems.
- Analysis of the waterwheel equations. Lorenz equations. Simple properties of the Lorenz
- Linearization. Jacobian matrix. Borderline cases. Example: Centers are delicate. Polar coordinates. Example of phase plane ...
- Global stability for the origin for r is less than 1. Liapunov function. Boundedness. Hopf bifurcations. No quasiperiodicity.
- Sketching phase planes is often a hard task, but the existence of a conservation law can greatly ease the process. In this lecture ...
- Hopf, saddle-node bifurcation of cycles, SNIPER, and homoclinic bifurcation. Coupled oscillators. Knotted cycles. Quasiperiodicity ...
In-Depth Information on Mae5790 7 Conservative Systems
Mechanical Phase plane analysis. Eigenvectors and eigenvalues. Classification of 2-D linear Techniques for ruling out closed orbits: index theory and Dulac's criterion. Techniques for proving closed orbits exist: ... Equations of motion. When can we neglect the second derivative? Dimensional analysis and scaling. A singular limit. Reading: ...
Index of a curve (with respect to a given vector field). Properties of the index. Index of a point. Using index theory to rule out closed ...
That wraps up our extensive overview of Mae5790 7 Conservative Systems.