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