Add implicit integrator.

Added analytic derivatives of smooth (unconstrained) dynamics forces, with respect to velocities:
  - Centripetal and Coriolis forces computed by the Recursive Newton-Euler algorithm.
  - Damping and fluid-drag passive forces.
  - Actuation forces.

A new implicit-in-velocity integrator is implemented using the analytic derivatives. This integrator lies between the Euler and Runge Kutta integrators in terms of both stability and computational cost.

PiperOrigin-RevId: 450377010
Change-Id: Ie192b441876c22e732fb749333926f296e0a09cc

src/xml/xml_native_reader.cc

@@ -416,10 +416,11 @@ const mjMap camlight_map[camlight_sz] = {
 
 
 // integrator type
-const int integrator_sz = 2;
+const int integrator_sz = 3;
 const mjMap integrator_map[integrator_sz] = {
   {"Euler",       mjINT_EULER},
-  {"RK4",         mjINT_RK4}
+  {"RK4",         mjINT_RK4},
+  {"implicit",    mjINT_IMPLICIT}
 };