Modelica Example - Second Order Equation

//Second order equation (rotating object, torsion spring, damping)

within ModelicaByExample.BasicEquations.RotationalSMD;

model SecondOrderSystem "A second order rotational system"

  type Angle=Real(unit="rad");

  type AngularVelocity=Real(unit="rad/s");

  type Inertia=Real(unit="kg.m2");

  type Stiffness=Real(unit="N.m/rad");

  type Damping=Real(unit="N.m.s/rad");

  parameter Inertia J1= 0.4 "Moment of inertia for inertia 1" ;// Moment of inertia 

  parameter Inertia J2=1.0"Moment of inertia for inertia 2"; 

  parameter Stiffness k1= 11 "Spring constant for spring 1" ;//spring stiffness 

  parameter Stiffness k2=5"Spring constant for spring 2"; 

  parameter Damping d1=0.2"Damping for damper 1";//阻尼 

  parameter Damping d2=1.0"Damping for damper 2"; 

  Angle phi1 "Angle for inertia 1";

  Angle phi2 "Angle for inertia 2";

  AngularVelocity omega1 "Velocity of inertia 1";

  AngularVelocity omega2 "Velocity of inertia 2";

initial equation//initialization equation 

  phi1 = 0 ;

  phi2 = 1;

  omega1 = 0 ;

  omega2 = 0 ;

equation

  // Equations for inertia 1

  omega1 = der (phi1);//Kinematics relationship between angular velocity and angle

  J1* der (omega1) = k1*(phi2-phi1)+d1* der (phi2-phi1);//Dynamic relationship between angular velocity and torque

  // Equations for inertia 2

  omega2 = the (phi2);

  J2* der (omega2) = k1*(phi1-phi2)+d1* der (phi1-phi2)-k2*phi2-d2* der (phi2);

end SecondOrderSystem;