Library of Examples

 
We collect several examples of linear systems to which we apply OreModules. The following list provides Maple worksheets that deal with these examples. It is sorted by the type of the equations which describe the linear system (i.e. ordinary differential equations, differential time-delay systems, partial differential equations).
 
In a table below, the list of worksheets is also sorted by the features of OreModules that are applied to the linear systems.
 

Ordinary Differential Systems

Description Maple Worksheet Text version Reference
Bipendulum Bipendulum.mws Bipendulum.pdf Pommaret (2001)
Two Pendula mounted on a Cart TwoPendula.mws TwoPendula.pdf Polderman, Willems (1998)
Differential Algebraic Equations LinDAE.mws LinDAE.pdf Le Vey (1998)
RLC Circuit RLC-circuit.mws RLC-circuit.pdf Pommaret (2001)
Time-varying Ordinary Differential Equations TimeVar.mws TimeVar.pdf Sontag (1990)
One-wheeled Bicycle Pedalvit.mws Pedalvit.pdf Quadrat, Viot (1999)
Rolling Sphere Sphere.mws Sphere.pdf Hadamard (1901)
 

Differential Time-delay Systems

Description Maple Worksheet Text version Reference
Two Reflector Antenna Antenna.mws Antenna.pdf Mounier (1995)
Electric Transmission Line ElectricLine.mws ElectricLine.pdf Mounier (1995)
LC Transmission Line LCTransmission.mws LCTransmission.pdf Rasvan, Niculescu (2002)
Flexible Arm FlexibleArm.mws FlexibleArm.pdf Benosman, Le Vey (2000)
Flexible Rod FlexibleRod.mws FlexibleRod.pdf Mounier (1995)
High Speed Network Network.mws Network.pdf Fliess, Mounier (1998)
Satellite Satellite.mws Satellite.pdf Kailath (1980),
Mounier (1995)
Stirred Tank StirredTank.mws StirredTank.pdf Kwakernaak, Sivan (1972)
Vibrating String String.mws String.pdf Mounier et al. (1998)
Wind Tunnel Model Windtunnel.mws Windtunnel.pdf Manitius (1984)
Saint-Venant equations SaintVenant.mws SaintVenant.pdf Dubois et al. (1999),
Petit, Rouchon (2002)
Process Model ProcessModel.mws ProcessModel.pdf Petit et al. (1997)
 

Partial Differential Systems

Description Maple Worksheet Text version Reference
Einstein Equations Einstein.mws Einstein.pdf Pommaret (1995),
Weyl (1952)
Maxwell Equations Maxwell.mws Maxwell.pdf Weyl (1952)
Elasticity Elasticity.mws Elasticity.pdf Pommaret (2001),
Landau, Lifschitz (1990)
Lie-Poisson Structure: Lie algebra E2 LiePoissonE2.mws LiePoissonE2.pdf Bender et al. (2000),
Seiler (2003)
Lie-Poisson Structure: Lie algebra SU2 LiePoissonSU2.mws LiePoissonSU2.pdf Bender et al. (2000)
Linearized Euler Equations,
Boussinesq stationary system		 Euler.mws Euler.pdf Pommaret (1994)
Splitting of D1*div Splitting.mws Splitting.pdf Quadrat, Robertz (2005)
Identities of differential operators Identities.mws Identities.pdf Chorin, Marsden (1993)
 

Discrete-time Systems

Description Maple Worksheet Text version Reference
Stirred Tank StirredTank.mws StirredTank.pdf Kwakernaak, Sivan (1972)
Metal Rolling Process MetalRolling.mws MetalRolling.pdf Galkowski et al. (2003)
 
 
This Library of Examples is under construction. More worksheets dealing with various types of linear systems will be available soon.  
 
 

Library of Examples (sorted by system type and features)

 
Example for ... Ordinary Differential Systems Differential Time-delay Systems Partial Differential Systems Discrete-time Systems
Parametrization Bipendulum / Two Pendula mounted on a Cart / Differential Algebraic Equations / RLC Circuit / Rolling Sphere / Time-varying Ordinary Differential Equations / One-wheeled Bicycle Two Reflector Antenna / Electric Transmission Line / LC Transmission Line / Flexible Arm / Flexible Rod / High Speed Network / Saint-Venant equations / Satellite / Stirred Tank / Vibrating String / Wind Tunnel Model Einstein Equations / Maxwell Equations / Elasticity / Identities of differential operators / Lie-Poisson Structure: Lie algebra E2 / Lie-Poisson Structure: Lie algebra SU2 / Splitting of D1*div Stirred Tank / Metal Rolling Process
Minimal parametrization Time-varying Ordinary Differential Equations High Speed Network / Vibrating String / Satellite Maxwell Equations / Identities of differential operators  
Flat output Bipendulum / Two Pendula mounted on a Cart / RLC Circuit / Differential Algebraic Equations / Time-varying Ordinary Differential Equations / One-wheeled Bicycle Flexible Arm / Flexible Rod / Satellite / Stirred Tank   Stirred Tank
π-polynomial   Two Reflector Antenna / Electric Transmission Line / LC Transmission Line / Flexible Arm / Flexible Rod / High Speed Network / Vibrating String / Satellite / Stirred Tank / Wind Tunnel Model / Process Model   Stirred Tank
Brunovský canonical form Bipendulum / Two Pendula mounted on a Cart / RLC Circuit / Time-varying Ordinary Differential Equations / One-wheeled Bicycle Flexible Arm / Satellite / Stirred Tank   Stirred Tank
Torsion elements Bipendulum / Two Pendula mounted on a Cart / RLC Circuit Flexible Arm / Flexible Rod / Saint-Venant equations / Satellite / Stirred Tank Einstein Equations / Elasticity / Identities of differential operators / Lie-Poisson Structure: Lie algebra E2 / Lie-Poisson Structure: Lie algebra SU2 / Linearized Euler Equations / Splitting of D1*div Stirred Tank
Autonomous elements Bipendulum / Two Pendula mounted on a Cart / Rolling Sphere Flexible Arm / Satellite / Stirred Tank Elasticity Stirred Tank
Left/Right inverse Bipendulum / Two Pendula mounted on a Cart / Differential Algebraic Equations / RLC Circuit / Rolling Sphere / Time-varying Ordinary Differential Equations / One-wheeled Bicycle Flexible Arm / Flexible Rod / Saint-Venant equations / Satellite / Stirred Tank / Process Model Splitting of D1*div Stirred Tank / Metal Rolling Process
Generalized inverse Time-varying Ordinary Differential Equations Flexible Rod    
Integration of torsion elements Rolling Sphere      
Complement of the torsion submodule Rolling Sphere Saint-Venant equations Splitting of D1*div  
First integral Bipendulum / Two Pendula mounted on a Cart / RLC Circuit / Rolling Sphere Flexible Arm / Satellite / Stirred Tank   Stirred Tank
Approximation of a nonlinear system Bipendulum LC Transmission Line / Stirred Tank   Stirred Tank
System involving rational coefficients Differential Algebraic Equations / Time-varying Ordinary Differential Equations   Lie-Poisson Structure: Lie algebra E2 / Lie-Poisson Structure: Lie algebra SU2  
Motion planning One-wheeled Bicycle Stirred Tank / Wind Tunnel Model   Stirred Tank
Linear quadratic optimization problem One-wheeled Bicycle Stirred Tank   Stirred Tank
Controllability matrix Time-varying Ordinary Differential Equations Stirred Tank   Stirred Tank
 
 
This Library of Examples is under construction. More worksheets dealing with various types of linear systems will be available soon.