Break up engine_derivative.c into analytical and finite-differencing functions (moved to engine_derivative_fd.c)

PiperOrigin-RevId: 517165392
Change-Id: I649f5521364877d36d7564bb650a889298f0c8a1

src/engine/engine_derivative_fd.h

@@ -0,0 +1,43 @@
+// Copyright 2022 DeepMind Technologies Limited
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#ifndef MUJOCO_SRC_ENGINE_ENGINE_DERIVATIVE_FD_H_
+#define MUJOCO_SRC_ENGINE_ENGINE_DERIVATIVE_FD_H_
+
+#include <mujoco/mjdata.h>
+#include <mujoco/mjexport.h>
+#include <mujoco/mjmodel.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+// centered finite difference approximation to mjd_smooth_vel
+MJAPI void mjd_smooth_velFD(const mjModel* m, mjData* d, mjtNum eps);
+
+// add forward finite difference approximation of (d qfrc_passive / d qvel) to qDeriv
+MJAPI void mjd_passive_velFD(const mjModel* m, mjData* d, mjtNum eps);
+
+// advance simulation using control callback, skipstage is mjtStage
+MJAPI void mj_stepSkip(const mjModel* m, mjData* d, int skipstage, int skipsensor);
+
+// finite differenced transition matrices (control theory notation)
+MJAPI void mjd_transitionFD(const mjModel* m, mjData* d, mjtNum eps, mjtByte centered,
+                            mjtNum* A, mjtNum* B, mjtNum* C, mjtNum* D);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif  // MUJOCO_SRC_ENGINE_ENGINE_DERIVATIVE_FD_H_