Coordinate system: about

Principle of use

The coordinate systems are used to simplify the geometry description and the movement of the devices parts.

Types of coordinate systems: 2D domain

The different types of coordinate systems for 2D / 3D domain and associated coordinates are presented below:

2D Cartesian coordinate system Coordinates (x,y)	2D Cylindrical coordinate system Coordinates (r,θ)

Defined by propagation from another coordinate system

Types of coordinate systems: 3D domain

The different types of coordinate systems for 3D domain and associated coordinates are presented below:

3D Cartesian coordinate system Coordinates (x,y,z)	3D Cylindrical coordinate system Coordinates (r,θ,z)	3D Spherical coordinate system Coordinates (r,θ,φ)

Defined by propagation from another coordinate system

Reference coordinate systems

It is possible to distinguish the following coordinate systems:

• The global coordinate system is the coordinate system in which are performed the computations. It is inaccessible for the user. The global coordinate system is a universal Cartesian coordinate system using meter as length unit and degree as angle unit.

• The working coordinate systems are coordinate systems created by the user to cover the study needs.

  The working coordinate systems are defined:

  • with respect to the Global coordinate system, when they refer to the global coordinate system
  • with respect to a Local coordinate system, when they refer to other coordinate systems.

All the entities are defined in the working coordinate systems (user's coordinate systems) and are evaluated in the global coordinate system for calculations.

Example

To describe the device represented in the figure below, two geometric coordinate systems are used:

• A coordinate system for the description of the bar CART_BAR:

  Type: Cartesian

  Reference coordinate system: Global

  Specific characteristics:

  • length unit: millimeter
  • angle unit: degree
  Positioning:

  • center: 0,0,0
  • rotation: 0,0,0

• A coordinate system for the description of the torus CYL_TOR:

  Type: cylindrical

  Reference coordinate system: Local

  Specific characteristics:

  • Parent coordinate system: CART_BAR
  Positioning:

  • center: 0,0,0
  • rotation: 0,0,0

Positioning the coordinate system in its reference coordinate system

A coordinate system is positioned in its reference coordinate system using:

• the coordinates of the coordinate system center in its reference coordinate system
• the rotation angles of the axes of this coordinate system with respect to the axes of its reference coordinate system

Examples of positioning: 2D domain

Examples of positioning: 3D domain

Coordinate system units

The user can define the length and angle units for a coordinate system defined with respect to the global coordinate system.

A coordinate system defined with respect to the local coordinate system inherits the units of the reference coordinate system (parent coordinate system).

Parameter setting

The origin of coordinate system and the rotation angles about axes can be defined using algebraic expression. The algebraic expression can contain:

• constants
• geometric parameters (created beforehand)
• basic mathematical functions using operators: +, -, *, /, ( )
• usual mathematical functions admitted by Fortran.

The mathematical functions are described in section Functions.