diff --git a/gtsam/navigation/Scenario.h b/gtsam/navigation/Scenario.h
index 3324abaab..bc9dfe8eb 100644
--- a/gtsam/navigation/Scenario.h
+++ b/gtsam/navigation/Scenario.h
@@ -67,24 +67,26 @@ class ExpmapScenario : public Scenario {
   const Vector3 a_b_;  // constant centripetal acceleration in body = w_b * v_b
 };
 
-/// Accelerating from an arbitrary initial state
+/// Accelerating from an arbitrary initial state, with optional rotation
 class AcceleratingScenario : public Scenario {
  public:
-  /// Construct scenario with constant twist [w,v]
+  /// Construct scenario with constant acceleration in navigation frame and
+  /// optional angular velocity in body: rotating while translating...
   AcceleratingScenario(const Rot3& nRb, const Point3& p0, const Vector3& v0,
-                       const Vector3& accelerationInBody)
-      : nRb_(nRb), p0_(p0.vector()), v0_(v0), a_n_(nRb_ * accelerationInBody) {}
+                       const Vector3& a_n,
+                       const Vector3& omega_b = Vector3::Zero())
+      : nRb_(nRb), p0_(p0.vector()), v0_(v0), a_n_(a_n), omega_b_(omega_b) {}
 
   Pose3 pose(double t) const {
-    return Pose3(nRb_, p0_ + v0_ * t + a_n_ * t * t / 2.0);
+    return Pose3(nRb_.expmap(omega_b_ * t), p0_ + v0_ * t + a_n_ * t * t / 2.0);
   }
-  Vector3 omega_b(double t) const { return Vector3::Zero(); }
+  Vector3 omega_b(double t) const { return omega_b_; }
   Vector3 velocity_n(double t) const { return v0_ + a_n_ * t; }
   Vector3 acceleration_n(double t) const { return a_n_; }
 
  private:
   const Rot3 nRb_;
-  const Vector3 p0_, v0_, a_n_;
+  const Vector3 p0_, v0_, a_n_, omega_b_;
 };
 
 }  // namespace gtsam
diff --git a/gtsam/navigation/tests/testScenario.cpp b/gtsam/navigation/tests/testScenario.cpp
index c029ecc03..ab538e02a 100644
--- a/gtsam/navigation/tests/testScenario.cpp
+++ b/gtsam/navigation/tests/testScenario.cpp
@@ -16,7 +16,10 @@
  */
 
 #include <gtsam/navigation/Scenario.h>
+#include <gtsam/base/numericalDerivative.h>
+
 #include <CppUnitLite/TestHarness.h>
+#include <boost/bind.hpp>
 #include <cmath>
 
 using namespace std;
@@ -87,18 +90,25 @@ TEST(Scenario, Accelerating) {
   const Point3 P0(10, 20, 0);
   const Vector3 V0(50, 0, 0);
 
-  const double a_b = 0.2;  // m/s^2
-  const AcceleratingScenario scenario(nRb, P0, V0, Vector3(a_b, 0, 0));
+  const double a = 0.2;  // m/s^2
+  const Vector3 A(0, a, 0), W(0.1, 0.2, 0.3);
+  const AcceleratingScenario scenario(nRb, P0, V0, A, W);
 
   const double T = 3;
-  const Vector3 A = nRb * Vector3(a_b, 0, 0);
-  EXPECT(assert_equal(Vector3(0, 0, 0), scenario.omega_b(T), 1e-9));
+  EXPECT(assert_equal(W, scenario.omega_b(T), 1e-9));
   EXPECT(assert_equal(Vector3(V0 + T * A), scenario.velocity_n(T), 1e-9));
   EXPECT(assert_equal(A, scenario.acceleration_n(T), 1e-9));
 
+  {
+  // Check acceleration in nav
+  Matrix expected = numericalDerivative11<Vector3, double>(
+      boost::bind(&Scenario::velocity_n, scenario, _1), T);
+  EXPECT(assert_equal(Vector3(expected), scenario.acceleration_n(T), 1e-9));
+  }
+
   const Pose3 T3 = scenario.pose(3);
-  EXPECT(assert_equal(nRb, T3.rotation(), 1e-9));
-  EXPECT(assert_equal(Point3(10 + T * 50, 20 + a_b * T * T / 2, 0),
+  EXPECT(assert_equal(nRb.expmap(T * W), T3.rotation(), 1e-9));
+  EXPECT(assert_equal(Point3(10 + T * 50, 20 + a * T * T / 2, 0),
                       T3.translation(), 1e-9));
 }
 
diff --git a/gtsam/navigation/tests/testScenarioRunner.cpp b/gtsam/navigation/tests/testScenarioRunner.cpp
index b7a864016..8d01f5572 100644
--- a/gtsam/navigation/tests/testScenarioRunner.cpp
+++ b/gtsam/navigation/tests/testScenarioRunner.cpp
@@ -83,8 +83,9 @@ TEST(ScenarioRunner, Accelerating) {
   const Point3 P0(10, 20, 0);
   const Vector3 V0(50, 0, 0);
 
-  const double a_b = 0.2;  // m/s^2
-  const AcceleratingScenario scenario(nRb, P0, V0, Vector3(a_b, 0, 0));
+  const double a = 0.2;  // m/s^2
+  const Vector3 A(0, a, 0);
+  const AcceleratingScenario scenario(nRb, P0, V0, A);
 
   const double T = 3;  // seconds
   ScenarioRunner runner(&scenario, T / 10, kGyroSigma, kAccelerometerSigma);