**L**- :length
**T**- :time
**M**- :mass
**O**- :temperature

Examples are:

**v**- =velocity=[L]
- accel =
- force =
- frequency =

Theorem: Physical equations must be homogenous in all units.

general differential equation for , This means that if is the same, the solutions are the same. for gravity.

Buckingham PI theorem.

Transform equation to for unitless (homogenous degree 0). If contain r independent dimensions let . Set . Take the derivative with respect to , then set . You will get r equations with n unknowns. This means there is an which is dimensionless.

General case: where for u s.t. the are dimensionless.

Examples:

source psfile jl@crush.caltech.edu index