Numerically Linearizing a Dynamic System

In this video we show how to linearize a dynamic system using numerical techniques. In other words, the linearization process does not require an analytical description of the system. This is useful in situations where the system in question is either too complicated to describe with analytical functions or simply does not have an analytical representation (for example the system is a black-box that can only accept inputs and generate outputs). We review the theory of linearization before developing a numerical technique to perform the linearization. We then show how to verify our results with native Matlab/Simulink tools.

Topics and timestamps:
0:00 – Introduction
6:40 – Implicit form of nonlinear ODEs
15:20 – Linearization via Taylor Series Expansion
45:11 – Calculating partial derivatives using the symmetric difference quotient
1:02:38 – Example of linearizing the RCAM model
1:26:36 – Linearizing the RCAM model using Matlab/Simulink tools
1:32:05 – Analytically verifying linearization results
1:41:27 – Summary

Lecture notes and code can be downloaded from https://github.com/clum/YouTube/tree/...

All Flight Mechanics videos in a single playlist (   • Flight Mechanics  )

#FlightMechanics
#Linearization

You can support this channel via Patreon at   / christopherwlum   or by clicking on the ‘Thanks’ button underneath the video. Thank you for your help!