Drawing Phase Portraits for Nonlinear Systems

This video shows how to draw phase portraits and analyze fully nonlinear systems. Specifically, we identify all of the fixed points, linearize around these fixed points, analyze the stability with eigenvalues and eigenvectors, and then infer global nonlinear dynamics outside of these regions.

@eigensteve on Twitter

This video was produced at the University of Washington

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0:00 Overview and deriving equations from F=ma
4:30 Finding fixed points of system
8:35 Linearizing near fixed points
10:09 First fixed point: A linear center
12:24 Second fixed point: An unstable saddle
15:01 Drawing full global phase portrait
22:25 Adding friction and drawing phase portrait

[dafield_family]

i love the transparent table and the colors. truly a wonderful format to lure people into maths. great job

[albertopenacabana]

And finally here!! Thanks for this series of videos, Steve. The way you explain math, going to the deep meaning, giving the intuition behind each concept, is definitely the way to make people love math.

[philblandford]

I'm glad you corrected the name of the function, my brain was short-circuiting for a while there

[woodworkingaspirations]

Excellent teaching. Saved me going through several pages of a chapter.

[rajendramisir]

Brilliant explanation and reasoning through phase portraits without friction and with friction in a dynamical mechanical system.

[mikhail_koshelev]

Beautiful! Thank you a lot for the videos! I check the channel every day for new episodes. Hope you won't stop making more content in the future!

[malikialgeriankabyleswag]

You are a great man and a great teacher may God bless you! And thanks for providing this for us.

[AniruddhKrishna]

amazing video. I cant eeven stress on how much phase portraits have troubled me

[kasparondrej]

Your explanation was excellent! Thank you!

[CitadelLords]

Best math hours on this channel. Thanks man for the great work and love you are giving explanations!

[reubenemmanuel]

Finally the calculation makes sense. Thank you

[hoseinzahedifar]

This lecture is very interesting... Thank you very much.

[alirezaesmailnezhad]

This was very instructive and helpful.

[eugeniagomes]

Thaks for the explanaition, It was super clear!

What an understandable lecture! Thank you so much!

[williancintra]

Great class! My only question is: how can he write backwards like that?

[GeoffryGifari]

wait... the phase portrait kinda looks as if its a contour plot when we look at the potential "hills and valleys" from "above"

[surbhi]

Please also explain how to solve and draw phase portrait numerically like in MATLAB

[Giovanni]

How is the representation of trajectories in 3D space with t axis said in English?

[BalaramPradhan-if]

Thank you so much sir for such a nice explanations. Sir please make a video how to draw this graph in Mathematica or in Matlab