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

test/engine/testdata/derivative/tumbling_thin_object.xml

@@ -0,0 +1,17 @@
+<mujoco>
+  <option density="1.225" viscosity="1.8e-5" wind="0 0 1" integrator="implicit"/>
+
+  <worldbody>
+    <light pos="0 0 1"/>
+    <geom type="plane" size="1 1 .01" pos="0 0 -1"/>
+    <body>
+      <freejoint/>
+      <body>
+        <geom type="box" size=".025 .01 0.0001" pos=".025 0 0" euler="20 0 0" mass="1e-4"/>
+      </body>
+      <body>
+        <geom type="box" size=".025 .01 0.0001" pos="-.025 0 0" euler="-19 0 0" mass="1e-4"/>
+      </body>
+    </body>
+  </worldbody>
+</mujoco>