2.0 A better way to understand Differential Equations | Nonlinear Dynamics | 2D Linear Diff Eqns

Part 1:    • 1.0 A better way to understand Differ...  
Part 2:    • 2.0 A better way to understand Differ...  
Part 3:    • 3.0 A better way to understand Differ...  

These second-order linear differential equations can be written in the form
dx/dt = ax + by
dy/dt = cx + dy
Depending on the values of a,b,c and d, the dynamics will be very different! They can be characterized by finding the eigenvalues and eigenvectors of the matrix A = [a, b; c, d]. This is a necessary first step to getting qualitative pictures about nonlinear 2nd order differential equations - something we'll talk about in part 3.

Chapters:
0:00 Intro & Recap
0:27 Spring Mass Damper Equation of Motion
1:25 Spring Mass Damper Vector Field
2:28 Spring Mass Damper State Space form
2:58 General Solution to Linear System
5:17 Saddle Example
7:02 Characterization of Linear Systems from Eigenvalues
8:23 Summary Animations & Outro

Music:
Music by Vincent Rubinetti
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/a...
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjw...

Other Music:
Nuclear Lynx - Discovery