Physics.Learn.StateSpace

A StateSpace is an affine space where the associated vector space has scalars that are instances of Fractional. If p is an instance of StateSpace, then the associated vectorspace Diff p is intended to represent the space of time derivatives of paths in p.

StateSpace is very similar to Conal Elliott's AffineSpace.

Documentation

class (VectorSpace (Diff p), Fractional (Scalar (Diff p))) => StateSpace p where

A StateSpace has an associated vector space, the vectors of which can be multiplied or divided by scalars. An example would be the set of positions of a particle. Position is not a vector, but displacement (difference in position) is a vector.

Associated Types

type Diff p

Associated vector space

Methods

(.-.) :: p -> p -> Diff p

Subtract points

(.+^) :: p -> Diff p -> p

Point plus vector

Instances

StateSpace Double

StateSpace Vec

StateSpace Position

(StateSpace p, StateSpace q, ~ * (Time p) (Time q)) => StateSpace (p, q)

(StateSpace p, StateSpace q, StateSpace r, ~ * (Time p) (Time q), ~ * (Time q) (Time r)) => StateSpace (p, q, r)

(.-^) :: StateSpace p => p -> Diff p -> p

Point minus vector

type Time p = Scalar (Diff p)

The scalars of the associated vector space can be thought of as time intervals.