learn-physics-0.2: Haskell code for learning physics

Stabilityexperimental
MaintainerScott N. Walck <walck@lvc.edu>
Safe HaskellTrustworthy

Physics.Learn.Position

Description

A module for working with the idea of position and coordinate systems.

Synopsis

Documentation

data Position Source

A type for position. Position is not a vector because it makes no sense to add positions.

Instances

type Displacement = VecSource

A displacement is a vector.

type ScalarField = Position -> DoubleSource

A scalar field associates a number with each position in space.

type VectorField = Position -> VecSource

A vector field associates a vector with each position in space.

type Field v = Position -> vSource

Sometimes we want to be able to talk about a field without saying whether it is a scalar field or a vector field.

type CoordinateSystem = (Double, Double, Double) -> PositionSource

A coordinate system is a function from three parameters to space.

cartesian :: CoordinateSystemSource

The Cartesian coordinate system. Coordinates are (x,y,z).

cylindrical :: CoordinateSystemSource

The cylindrical coordinate system. Coordinates are (s,phi,z), where s is the distance from the z axis and phi is the angle with the x axis.

spherical :: CoordinateSystemSource

The spherical coordinate system. Coordinates are (r,theta,phi), where r is the distance from the origin, theta is the angle with the z axis, and phi is the azimuthal angle.

cartSource

Arguments

:: Double

x coordinate

-> Double

y coordinate

-> Double

z coordinate

-> Position 

A helping function to take three numbers x, y, and z and form the appropriate position using Cartesian coordinates.

cylSource

Arguments

:: Double

s coordinate

-> Double

phi coordinate

-> Double

z coordinate

-> Position 

A helping function to take three numbers s, phi, and z and form the appropriate position using cylindrical coordinates.

sphSource

Arguments

:: Double

r coordinate

-> Double

theta coordinate

-> Double

phi coordinate

-> Position 

A helping function to take three numbers r, theta, and phi and form the appropriate position using spherical coordinates.

cartesianCoordinates :: Position -> (Double, Double, Double)Source

Returns the three Cartesian coordinates as a triple from a position.

cylindricalCoordinates :: Position -> (Double, Double, Double)Source

Returns the three cylindrical coordinates as a triple from a position.

sphericalCoordinates :: Position -> (Double, Double, Double)Source

Returns the three spherical coordinates as a triple from a position.

displacementSource

Arguments

:: Position

source position

-> Position

target position

-> Displacement 

Displacement from source position to target position.

shiftPosition :: Displacement -> Position -> PositionSource

Shift a position by a displacement.

shiftObject :: Displacement -> (a -> Position) -> a -> PositionSource

An object is a map into Position.

shiftField :: Displacement -> (Position -> v) -> Position -> vSource

A field is a map from Position.

addFields :: AdditiveGroup v => [Field v] -> Field vSource

Add two scalar fields or two vector fields.

rHat :: VectorFieldSource

The vector field in which each point in space is associated with a unit vector in the direction of increasing spherical coordinate r, while spherical coordinates theta and phi are held constant. Defined everywhere except at the origin. The unit vector rHat points in different directions at different points in space. It is therefore better interpreted as a vector field, rather than a vector.

thetaHat :: VectorFieldSource

The vector field in which each point in space is associated with a unit vector in the direction of increasing spherical coordinate theta, while spherical coordinates r and phi are held constant. Defined everywhere except on the z axis.

phiHat :: VectorFieldSource

The vector field in which each point in space is associated with a unit vector in the direction of increasing (cylindrical or spherical) coordinate phi, while cylindrical coordinates s and z (or spherical coordinates r and theta) are held constant. Defined everywhere except on the z axis.

sHat :: VectorFieldSource

The vector field in which each point in space is associated with a unit vector in the direction of increasing cylindrical coordinate s, while cylindrical coordinates phi and z are held constant. Defined everywhere except on the z axis.

xHat :: VectorFieldSource

The vector field in which each point in space is associated with a unit vector in the direction of increasing Cartesian coordinate x, while Cartesian coordinates y and z are held constant. Defined everywhere.

yHat :: VectorFieldSource

The vector field in which each point in space is associated with a unit vector in the direction of increasing Cartesian coordinate y, while Cartesian coordinates x and z are held constant. Defined everywhere.

zHat :: VectorFieldSource

The vector field in which each point in space is associated with a unit vector in the direction of increasing Cartesian coordinate z, while Cartesian coordinates x and y are held constant. Defined everywhere.