Control-Network-Systems/docs/Formularies/PHYSICS-FORMULARY.md

Physics Formulary

Tip

You'll often see \vec{v} and \vec{\dot x}, and \vec{a} and \vec{\ddot{x}}.

These are equal, but the latter forms, express better the relation between state space variables

Hooke's Law (AKA Spring Formula)

\vec{F} = -k\vec{x}

• k: Spring Constant
• \vec{x}: vector of spring stretch from rest position

Fluid drag

\vec{F_D} = \frac{1}{2}b\vec{v}^2C_{D}A

• b: density of fluid
• v: speed of object relative to the fluid
• C_D: drag coefficient
• A: cross section area

Stokes Drag

\vec{F_D} = -6 \pi R\mu \vec{v}

• \mu: dynamic viscosity
• R: radius (in meters) of the sphere
• \vec{v}: flow velocity relative to the fluid

Simplified Fluid Drag (Simplified Stokes Equation)

\vec{F_D} = -b \vec{v}

• b: simplified coefficient that has everything else
• \vec{v}: flow velocity relative to the fluid

Newton force