Name: Lagrange

Author: Peter Selinger

Version: 0.15

Documentation: http://www.mathstat.dal.ca/~selinger/lagrange/

The Lagrange Applet has eight general parameters that determine the basic functions of the applet. In addition, for each specific physical system (such as, a double pendulum) there is a set of parameters that determine the physical properties and initial condition of the system.

Name | Possible Values | Description |

type | DoublePendulum, SpringPendulum, DoubleSpring
| Physical system to be displayed. |

frames | a positive integer (10)
| Number of frames per second. |

timefactor | a decimal fraction (1.0)
| Time factor for slow or fast motion. |

trace | true, false
| Draw a trace? |

controls | true, false
| Display a panel of control buttons? |

showenergy | true, false
| Display the total energy? |

constrainenergy | true, false
| Enforce energy preservation? |

energycontrol | true, false
| Display button to toggle energy preservation? |

deterministic | true, false
| Deterministic simulation? |

bgcolor | #xxxxxx (getBackground())
| The background color. |

fgcolor | #xxxxxx (#000000)
| The foreground color. |

tracecolor | #xxxxxx (#ffffff)
| The color of the trace. |

scalecolor | #xxxxxx (#000000)
| The color of the metric scale. |

timecolor | #xxxxxx (#000000)
| The color of the time scale. |

energycolor | #xxxxxx (#000000)
| The color of the energy display. |

Name | Default | Description |

m0 | 2 | inner mass, in kg |

m1 | 3 | outer mass, in kg |

l0 | 6 | inner length, in m |

l1 | 4 | outer length, in m |

g | 9.81 | gravity, in m/s^2 |

alpha | 2.2 | initial value for angle of inner leg, counterclockwise from south, in radians |

alpha' | 0 | initial derivative for angle of inner leg, counterclockwise from south, in radians |

beta | 3 | initial value for angle of outer leg, counterclockwise from south, in radians |

beta' | 0 | initial derivative for angle of outer leg, counterclockwise from south, in radians |

Name | Default | Description |

m | 1 | mass, in kg |

l0 | 1 | first spring length, in m |

l1 | 1 | second spring length, in m |

k0 | 5 | first spring constant, in N/m |

k1 | 1 | second spring constant, in N/m |

b | 1.9 | distance between pivot points, in m |

g | 0 | gravity, in m/s^2 |

x | 1.2 | initial value for coordinate of mass, to right of midpoint of pivots, in m |

x' | 0 | initial derivative for coordinate of mass, to right of midpoint of pivots, in m |

y | 1 | initial value for coordinate of mass, above midpoint of pivots, in m |

y' | 0 | initial derivative for coordinate of mass, above midpoint of pivots, in m |

Name | Default | Description |

m0 | 2 | inner mass, in kg |

m1 | 1 | outer mass, in kg |

l0 | 6 | inner length, in m |

l1 | 4 | outer length, in m |

k0 | 60 | spring constant, in N/m |

g | 9.81 | gravity, in m/s^2 |

x | 2.2 | initial value for coordinate of inner mass, right of pivot, in m |

x' | 0 | initial derivative for coordinate of inner mass, right of pivot, in m |

y | 3 | initial value for coordinate of inner mass, above pivot, in m |

y' | 0 | initial derivative for coordinate of inner mass, above pivot, in m |

alpha | 1 | initial value for angle of outer leg, counterclockwise from south, in radians |

alpha' | 0 | initial derivative for angle of outer leg, counterclockwise from south, in radians |

<applet codebase=http://www.mathstat.dal.ca/~selinger/lagrange/codebase code=Lagrange.class width=350 height=350> <param name=type value=DoublePendulum> <param name=frames value=10> <param name=trace value=true> <param name=controls value=true> <param name=bgcolor value=#ffffcc> <param name=fgcolor value=#000000> <param name=tracecolor value=#ff0000> <param name=scalecolor value=#0000ff> </applet>

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