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/CMakeLists.txt

@@ -28,6 +28,8 @@ set(MUJOCO_ENGINE_SRCS
     engine_core_smooth.c
     engine_core_smooth.h
     engine_crossplatform.h
+    engine_derivative.c
+    engine_derivative.h
     engine_file.c
     engine_file.h
     engine_forward.c