János Karsai

Models of Impulsive Phenomena

Mathematica experiments

Typotex Publishing Company, Budapest, 2002

Special Mathematica package

Solving differential equations: ODESolve package

ODEGen[vec,var]

Generates ODE from the formula of the direction field for Dsolve

ICGen[IC,t0,var]

Generates initial condition equations Dsolve

FGen[var,t]

Generates function from the variables

ODEICGen[vec,IC,t0,var]

Generates initial-value for DSolve

ODESolve[xdot,var,IC,{t,t0,T},opt]

Solves ODE with several initial conditions

Impulsive systems with fixted impulse instances: IDESolve package

IDESolve[xdot,var,tn,Imp,IC,{t,t0,T},opt]

Solves an impulsive system with fixed impulse instances with several initial conditions

General impulsive systems: IDESolve  package

IDERKSolve[xdot,Impulse,var,IC,{t,t0,t1,dt}]

Solves a general  impulsive system

Visualization of impulzes: ImpulsePlot package

PlotFixedImpulseField[ Imp,tn,NN,{x,x0,x1,dx},opt]

Visualization of a scalar Imp impulsefield  in the tx Cartesian system

AnimateImpulse[Imp,tn,NN,{x,x0,x1},opt]

Animation of a scalar   impulse-mapping  by the elements of the list  tn

StackImpulse[Imp,tn,NN,{x,x0,x1},opt]

Visualization of a scalar  impulse-mapping  in the xx Cartesian system

ContourFieldPlot2D[ surf,fld,{x,x0,x1},{y,y0,y1},

{ContourOpt,FieldOpt,ShowOpt}]

Plot the elements of the field fld starting out of the contourline surf=0

PlotFixedImpulseField3D[ Imp,tn,NN,{x,x0,x1,dx},

{y,y0,y1,dy},opt]

Plotting the planar impulsefield  Imp  in the txy Cartesian system

JumpPlot[SS,II,{t, t0, t1},{x, x0, x1},opt]

The curve SS=0 its image by the impulse II in the  tx Cartesian system

JumpPlot3D[SS,II,{t,t0,t1},{x,x0,x1},{y,y0,y1},opt]

The surface SS=0 its image by the impulse II in the  txy Cartesian system

AutonomousJumpPlot2D[ SS,II,{x,x0,x1},{y,y0,y1},opt]

The impulse II on the curve SS =0   xy Cartesian system

AutonomousJumpPlot3D[ SS,II,{x,x0,x1},{y,y0,y1},opt]

The impulse II on the surface SS=0   xy Cartesian system

Plotting solutions and trajectories: Phase2D package

ParametricPlotColor[ xy,{t,t0,t1},opt]

Colored ParametricPlot

PhasePlot[Traj,{t,t0,t1},par],

PhasePlotBW[Traj,{t,t0,t1},par]

Plotting (black) a family of planar parametric curves

ListPhasePlot[sol,lineopt,opt]

Plotting a family of planar parametric curves given in a list

PhaseMap[Traj,{t,t1},lineopt,opt]

Phasemap of a family of planar parametric curves at the instant  t1

PhaseMap[Traj,{t,t0,t1,dt},opt]

Phasemaps of a family of planar parametric curves on the interval [t0 ,t1]

PhaseMapImp[Traj,{t,t1},lineopt,opt]

Phasemap of  an impulsive family of trajectories at the instants  t1-0 and t1+0

PhaseMapImp[Traj,{t,tn},lineopt,opt]

Phasemaps of  an impulsive family of trajectories at the instants  tn[[i]]-0 and tn[[i]]+0

ListPhaseMap[Traj,{t,t1},opt]

Phasemap of a family of planar parametric curves at the instant  t1

ListPhaseMap[Traj,{t,t0,t1,dt},opt]

Phasemaps of a family of planar parametric curves  on the interval [t0 ,t1]

SolCoordPlot[Traj,{t,t0,T},Icoord,opt]

Plot of  the coordinates

SolPlot[Traj,{t,t0,T},label,opt]

Plot of the coordinates of the members of a family of parametric curves in a graphic array

ListSolPlot[sol,Label,opt]

Plot of the coordinates of parametric curves  given in list  in a graphic  array

SolPlot3D[Traj,{t,t0,T},opt],

SolPlot3DBW[Traj,{t,t0,T},opt]

Colored  (BW) plotting of curves of form  {t, Traj} in 3D

ListSolPlot3D[sol,lineparm,opt]

Plot of the coordinates of 3D parametric curves  given in list

PhaseVol[Traj,{t,t1},lineopt,opt]

The phasemap of a family of parametric curves of form {t ,Traj} at the instant  t1

PhaseVol[Traj,{t,t0,t1,dt},lineopt,opt],

PhaseVolBW[Traj,{t,t0,t1,dt},lineopt,opt]

The phasemap of a family of parametric curves of form {t,Traj} on the interval the  [t0,t1]

PhaseVolImp[Traj,{t,t1},lineopt,opt]

Phasemaps of an impulsive  family of parametric curves {t,Traj }   at t1-0 és t1+0

PhaseVolImp[Traj,{t,tn},lineopt,opt],

PhaseVolImpBW[Traj,{t,tn},lineopt,opt]

Phasemaps of animpulsive  family of parametric curves {t,Traj} at the elements of the list tn

PlotContourLine3D[ f,{x,x0,x1},{y,y0,y1},{t,t0,t1,dt},opt]

Contourlines of the function   f at the planes  t =const

Some other functions: Spcecial.m package

JMf[f,var]

Derivative matrix of the function f  with respect to the elements of the list var

Tracef[Mf]

The tracew of the function  f

Coordinate[data,{n,m}]

Chosing two coordinates from the list data

ListPlot1[data,opt]

Several ListPlots in one figure