[ODE] Energy Status

[Jaroslav Sinecky]

Just from top of my head ....
isn't rotational energy something more like:

er = 0.5 * o(t) * I * o

where o is rotational velocity vector and o(t) is the same but transposed
which I think is not the same as 0.5 * I * (o * o). I and o should be in the
same coordinate system, so I think it's correct to transform to body local
system.

Cheers,
Jaroslav


> -----Original Message-----
> From: ode-bounces at q12.org [mailto:ode-bounces at q12.org]On Behalf
> Of Bill Sellers
> Sent: Sunday, March 19, 2006 10:07 PM
> To: ode-list
> Subject: [ODE] Energy Status
>
>
> Dear All,
>
> I want to calculate the energy status of the bodies in my simulation
> and whilst I think the following is right I'd really appreciate it if
> someone who's 3D physics wasn't as rusty as mine could take a look at
> the following (very straightforward) code.
>
> I'm pretty damn certain that linear kinetic is right, and I think
> that gravitational potential energy is OK too but the rotational
> kinetic energy could easily be wrong (I'm getting the rotational
> velocity in body local coordinates, squaring the individual values,
> multiplying it by the inertial tensor, summing the values and halving
> the whole thing). I've checked that it gives sensible results in
> simple test cases (i.e. effectively 2D) but I've no idea whether I
> get the right answer when I'm not using the principle moments of
> inertia and I'm a bit worried that there are interaction terms with
> linear and kinetic velocity that I might have to deal with (although
> I have always though they were independent when the centre of mass
> was used as the origin).
>
> If the code happens to be right then these might make useful
> functions...
>
> Cheers
> Bill
>
> dReal Body::GetRotationalKineticEnergy()
> {
>
>      // rotational KE = 0.5 I omega^2
>      dMass mass;
>      dBodyGetMass(m_BodyID, &mass);
>
>      const dReal *ow = dBodyGetAngularVel(m_BodyID);
>      dVector3 o;
>      dBodyVectorFromWorld (m_BodyID, ow[0], ow[1], ow[2], o);
>
>      dVector3 oo;
>      oo[0] = o[0] * o[0]; oo[1] = o[1] * o[1]; oo[2] = o[2] * o[2];
>      dVector3 rke;
>      dMULTIPLYOP0_331(rke, =, mass.I, oo);
>      dReal rotationalKE = 0.5 * (rke[0] + rke[1] + rke[2]);
>
>      return rotationalKE;
> }
>
> dReal Body::GetLinearKineticEnergy()
> {
>      // linear KE = 0.5 m v^2
>      dMass mass;
>      dBodyGetMass(m_BodyID, &mass);
>
>      const dReal *v = dBodyGetLinearVel(m_BodyID);
>      dReal linearKE = 0.5 * mass.mass * (v[0]*v[0] + v[1]*v[1] + v[2]
> *v[2]);
>
>      return linearKE;
> }
>
> dReal Body::GetGravitationalPotentialEnergy()
> {
>      dMass mass;
>      dBodyGetMass(m_BodyID, &mass);
>      dVector3 g;
>      dWorldGetGravity (m_WorldID, g);
>      const dReal *p = dBodyGetPosition(m_BodyID);
>
>      // gravitational PE = mgh
>      dReal gravitationalPotentialEnergy = - mass.mass * (g[0]*p[0] + g
> [1]*p[1] + g[2]*p[2]);
>
>      return gravitationalPotentialEnergy;
> }
>
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