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/engine/engine_support.h

@@ -98,6 +98,13 @@ MJAPI void mj_mulM2(const mjModel* m, const mjData* d, mjtNum* res, const mjtNum
 MJAPI void mj_addM(const mjModel* m, mjData* d, mjtNum* dst,
                    int* rownnz, int* rowadr, int* colind);
 
+// construct sparse matrix representations matching qM
+MJAPI void mj_makeMSparse(const mjModel* m, mjData* d, int *rownnz, int *rowadr, int *colind);
+
+// set dst = qM, handle different sparsity representations
+MJAPI void mj_setMSparse(const mjModel* m, mjData* d, mjtNum* dst,
+                         const int *rownnz, const int *rowadr, const int *colind);
+
 
 //-------------------------- perturbations ---------------------------------------------------------