Math notes/Differential Equations/Systems and Phase PlanesLinear Systems and Eigenmodes — Cheat sheetCHEAT SHEET · FREELessonCheat sheet →Unit cheat sheet →Save as PDF ↓Choose “Save as PDF” in the print dialog.On this pageCore ruleWatch forCore ruleAv=λv ⟹ x(t)=eλtv.A\mathbf v=\lambda\mathbf v\implies\mathbf x(t)=e^{\lambda t}\mathbf v.Av=λv⟹x(t)=eλtv. Watch forEigenvectors describe state directions, which may mix quantities with different physical units. Define the state and scaling before interpreting a phase-plane angle as a physical angle.← PREVIOUS LESSONTransfer Functions, Poles and ResponseNEXT LESSON →Phase Portraits and Stability
Mr. Integral