of Self-Gravitating Systems

- All Mathematica functions begin with a capital letter and enclose arguments with square brackets.

Useful Mathematica Functions | |
---|---|

General Description | Mathematica Equivalent |

sin(x) | Sin[x] |

arcsin(x) | ArcSin[x] |

e^{x}
| E^x or Exp[x] |

ln(x) | Log[x] |

x^{1/2}
| Sqrt[x] |

- Parentheses are used to perform operations on quantities: a*(b + c).
- When using various coordinate systems, one must use the variables specific to the particular coordinate system. Often these include Greek letters which must be spelled out: {r, theta, phi} for the Spherical coordinate system.

Standard Coordinate Systems | |
---|---|

Coordinate System | Variables |

Bipolar | (u, v, z) |

Bispherical | (u, v, phi) |

Cartesian | (x, y, z) |

ConfocalEllipsoidal | (lambda, mu, nu) |

ConfocalParaboloidal | (lambda, mu, nu) |

Conical | (lambda, mu, nu) |

Cylindrical | (r, theta, z) |

EllipticCylindrical | (u, v, z) |

OblateSpheroidal | (xi, eta, phi) |

ParabolicCylindrical | (u, v, z) |

Paraboloidal | (u, v, phi) |

ProlateSpheroidal | (xi, eta, phi) |

Spherical | (r, theta, phi) |

Toroidal | (u, v, phi) |

- Vectors are written as lists {a, b, c, ...} where a, b, c, ... are the coefficients corresponding to
the appropriate unit vectors. For instance, the Mathematica equivalent of the vector Ae
_{1}+ Be_{2}+ Ce_{3}is {A, B, C} in the coordinate system whose unit vectors are e_{1}, e_{2}, and e_{3}.

x y z {-(-----------------), -(-----------------), -(-----------------)} 2 2 2 3/2 2 2 2 3/2 2 2 2 3/2 (x + y + z ) (x + y + z ) (x + y + z ) |

where the elements of the above list are the components of the vector corresponding to e_{x},
e_{y}, and e_{z}.

2 2 2 Csc[theta] (3 r Sin[theta] + 2 r Cos[theta] Sin[theta] - r Sin[phi] Sin[theta]) ---------------------------------------------------------------------------------- 2 r |