Last comment I hope

gtsam/geometry/Pose3.cpp

@@ -212,8 +212,8 @@ Pose3 Pose3::Expmap(const Vector6& xi, OptionalJacobian<6, 6> Hxi) {
     // We are creating a Pose3, so we still need to chain H with R^T, the
     // Jacobian of Pose3::Create with respect to t.
     const Matrix3 Q = R.matrix().transpose() * H;
-    *Hxi << Jr, Z_3x3,  //
-        Q, Jr;
+    *Hxi << Jr, Z_3x3,  // Jr here *is* the Jacobian of expmap
+        Q, Jr;  // Here Jr = R^T * J_l, with J_l the Jacobian of t in v.
   }
 
   return Pose3(R, t);

gtsam/navigation/NavState.cpp

@@ -138,9 +138,11 @@ NavState NavState::Expmap(const Vector9& xi, OptionalJacobian<9, 9> Hxi) {
     // We are creating a NavState, so we still need to chain H_t_w and H_v_w
     // with R^T, the Jacobian of Navstate::Create with respect to both t and v.
     const Matrix3 M = R.matrix();
-    *Hxi << Jr, Z_3x3, Z_3x3,  //
+    *Hxi << Jr, Z_3x3, Z_3x3,   // Jr here *is* the Jacobian of expmap
         M.transpose() * H_t_w, Jr, Z_3x3,  //
         M.transpose() * H_v_w, Z_3x3, Jr;
+        // In the last two rows, Jr = R^T * J_l, see Barfoot eq. (8.83).
+        // J_l is the Jacobian of applyLeftJacobian in the second argument.
   }
 
   return NavState(R, t, v);