Library of Examples

 
The following lists provide Mathematica worksheets (also available in .pdf) of several examples coming from mathematical physics, engineering sciences and control theory studied by means of OreAlgebraicAnalysis.
 

Linear ordinary differential systems

Description Mathematica Worksheet pdf version Reference
Kalman Example 1
Kalman1.nb
Kalman1.pdf
Brockett
Kalman Example 2
Kalman2.nb
Kalman2.pdf
Brockett
Bipendulum
Bipendulum.nb
Bipendulum.pdf
Pommaret
Two pendula
TwoPendula.nb
TwoPendula.pdf
Polderman-Willems
Time varying examples
TimeVarying.nb
TimeVarying.pdf
Sontag
 


Nonlinear ordinary differential systems via generic linearizations

Description Mathematica Worksheet pdf version Reference
Kinematic Car
KinematicCar.nb
KinematicCar.pdf
Martin-Murray-Rouchon
Car Model
CarModel.nb
CarModel.pdf
Martin-Murray-Rouchon
Non Holonomic Car
NonHolonomicCar.nb
NonHolonomicCar.pdf
Martin-Murray-Rouchon
 


Linear and nonlinear discrete systems

Description Mathematica Worksheet pdf version Reference
Discrete Example
DiscreteExample.nb
DiscreteExample.pdf
Kotta
Stirred Tank
StirredTank.nb
StirredTank.pdf
Kwakernaak-Sivan
 

Linear and nonlinear time-delay systems

Description Mathematica Worksheet pdf version Reference
Time-delay Example 1
TimeDelayExample1.nb
TimeDelayExample1.pdf
Marquez-Martinez
Time-delay Example 2
TimeDelayExample2.nb
TimeDelayExample2.pdf
Califano-Li-Moog
Time-delay Example 3
TimeDelayExample3.nb
TimeDelayExample3.pdf
Califano-Li-Moog
Time-delay Example 4
TimeDelayExample4.nb
TimeDelayExample4.pdf
Califano-Li-Moog
Tank Model 1
TankModel1.nb
TankModel1.pdf
Dubois-Petit-Rouchon
Tank Model 2
TankModel2.nb
TankModel2.pdf
Petit-Rouchon
Wind tunnel
WindTunnel.nb
WindTunnel.pdf
Manitius
Antenna
Antenna.nb
Antenna.pdf
MounierPhD
 

Partial differential systems

Description Mathematica Worksheet pdf version Reference
Maxwell Equations
Maxwell.nb
Maxwell.pdf
Weyl
Linear Elasticity
LinearElasticity.nb
LinearElasticity.pdf
Landau-Lifschitz,
Pommaret 2001
Einstein Equations
Einstein.nb
Einstein.pdf
Pommaret 1995,
Weyl
Lie-Poisson Structure
LiePoissonStructure.nb
LiePoissonStructure.pdf
Bender-Dunne-Mead
Lie Algebra SU(2)
LieAlgebraSU2.nb
LieAlgebraSU2.pdf
Bender-Dunne-Mead
Dirac Equations
Dirac.nb
Dirac.pdf
Courant-Hilbert
Classical PD system
ClassicalPDsystem.nb
ClassicalPDsystem.pdf
Polyanin
 

The library of examples is under construction. More worksheets will soon be available.