Giving Personality to Procedural Animations using Math

It's been a while since the last video hasn't it? I've made quite a bit of progress since the last update, and since one of the things I worked on was some procedurally animated characters, I decided to make a video about the subject. In particular, this video highlights the entire process from initial motivation, to the technical design, technical analysis, and game design considerations. Codeer's video on procedural animation: https://www.youtube.com/watch?v=e6Gjhr1IP6w Twitter thread about rope animation: https://twitter.com/t3ssel8r/status/1470039981502922752 Semi-implicit Newton's Method: https://en.wikipedia.org/wiki/Semi-implicit_Euler_method Verlet Integration: https://en.wikipedia.org/wiki/Verlet_integration Pole-Zero Matching: https://en.wikipedia.org/wiki/Matched_Z-transform_method Math animations made using the community-maintained version of manim: https://www.manim.community/ Timestamps: 0:00 intro 1:43 second order systems 7:03 implementation 8:55 testing 9:50 stability 13:30 conclusion Music: lofi geek - give me lofi geek - souls lofi geek - real lofi geek - two lifes lofi geek - lights