diff --git a/wpilibc/src/test/native/cpp/simulation/ElevatorSimTest.cpp b/wpilibc/src/test/native/cpp/simulation/ElevatorSimTest.cpp
index 3c647e6a25..8afcf6f654 100644
--- a/wpilibc/src/test/native/cpp/simulation/ElevatorSimTest.cpp
+++ b/wpilibc/src/test/native/cpp/simulation/ElevatorSimTest.cpp
@@ -66,7 +66,7 @@ TEST(ElevatorSimTest, MinMax) {
 
 TEST(ElevatorSimTest, Stability) {
   frc::sim::ElevatorSim sim{
-      frc::DCMotor::Vex775Pro(4), 100, 4_kg, 0.5_in, 0_m, 10_m, true};
+      frc::DCMotor::Vex775Pro(4), 100, 4_kg, 0.5_in, 0_m, 10_m, false};
 
   sim.SetState(frc::Vectord<2>{0.0, 0.0});
   sim.SetInput(frc::Vectord<1>{12.0});
diff --git a/wpilibj/src/test/java/edu/wpi/first/wpilibj/simulation/ElevatorSimTest.java b/wpilibj/src/test/java/edu/wpi/first/wpilibj/simulation/ElevatorSimTest.java
index fd2e7bab2e..b31769b5fd 100644
--- a/wpilibj/src/test/java/edu/wpi/first/wpilibj/simulation/ElevatorSimTest.java
+++ b/wpilibj/src/test/java/edu/wpi/first/wpilibj/simulation/ElevatorSimTest.java
@@ -91,7 +91,7 @@ class ElevatorSimTest {
   @Test
   void testStability() {
     var sim =
-        new ElevatorSim(DCMotor.getVex775Pro(4), 100, 4, Units.inchesToMeters(0.5), 0, 10, true);
+        new ElevatorSim(DCMotor.getVex775Pro(4), 100, 4, Units.inchesToMeters(0.5), 0, 10, false);
 
     sim.setState(VecBuilder.fill(0, 0));
     sim.setInput(12);
diff --git a/wpimath/src/main/java/edu/wpi/first/math/system/NumericalIntegration.java b/wpimath/src/main/java/edu/wpi/first/math/system/NumericalIntegration.java
index 94be369f14..e9b46fcbe1 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/system/NumericalIntegration.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/system/NumericalIntegration.java
@@ -238,7 +238,11 @@ public final class NumericalIntegration {
                     .times(h))
                 .normF();
 
-        h *= 0.9 * Math.pow(maxError / truncationError, 1.0 / 5.0);
+        if (truncationError == 0.0) {
+          h = dtSeconds - dtElapsed;
+        } else {
+          h *= 0.9 * Math.pow(maxError / truncationError, 1.0 / 5.0);
+        }
       } while (truncationError > maxError);
 
       dtElapsed += h;
diff --git a/wpimath/src/main/native/include/frc/system/NumericalIntegration.h b/wpimath/src/main/native/include/frc/system/NumericalIntegration.h
index bb856ece69..d2bf1222bb 100644
--- a/wpimath/src/main/native/include/frc/system/NumericalIntegration.h
+++ b/wpimath/src/main/native/include/frc/system/NumericalIntegration.h
@@ -122,7 +122,11 @@ T RKDP(F&& f, T x, U u, units::second_t dt, double maxError = 1e-6) {
                               (b1[6] - b2[6]) * k7))
                             .norm();
 
-      h *= 0.9 * std::pow(maxError / truncationError, 1.0 / 5.0);
+      if (truncationError == 0.0) {
+        h = dt.value() - dtElapsed;
+      } else {
+        h *= 0.9 * std::pow(maxError / truncationError, 1.0 / 5.0);
+      }
     } while (truncationError > maxError);
 
     dtElapsed += h;
diff --git a/wpimath/src/test/java/edu/wpi/first/math/system/NumericalIntegrationTest.java b/wpimath/src/test/java/edu/wpi/first/math/system/NumericalIntegrationTest.java
index 72fb5eab50..9b47148bf9 100644
--- a/wpimath/src/test/java/edu/wpi/first/math/system/NumericalIntegrationTest.java
+++ b/wpimath/src/test/java/edu/wpi/first/math/system/NumericalIntegrationTest.java
@@ -30,6 +30,20 @@ class NumericalIntegrationTest {
     assertEquals(Math.exp(0.1) - Math.exp(0.0), y1.get(0, 0), 1e-3);
   }
 
+  @Test
+  void testZeroRKDP() {
+    var y1 =
+        NumericalIntegration.rkdp(
+            (x, u) -> {
+              return VecBuilder.fill(0);
+            },
+            VecBuilder.fill(0),
+            VecBuilder.fill(0),
+            0.1);
+
+    assertEquals(0.0, y1.get(0, 0), 1e-3);
+  }
+
   @Test
   void testExponentialRKDP() {
     Matrix<N1, N1> y0 = VecBuilder.fill(0.0);
diff --git a/wpimath/src/test/native/cpp/system/NumericalIntegrationTest.cpp b/wpimath/src/test/native/cpp/system/NumericalIntegrationTest.cpp
index b1793adb9b..7c3d11621f 100644
--- a/wpimath/src/test/native/cpp/system/NumericalIntegrationTest.cpp
+++ b/wpimath/src/test/native/cpp/system/NumericalIntegrationTest.cpp
@@ -30,6 +30,16 @@ TEST(NumericalIntegrationTest, ExponentialWithU) {
   EXPECT_NEAR(y1(0), std::exp(0.1) - std::exp(0), 1e-3);
 }
 
+// Tests that integrating dx/dt = 0 works with RKDP
+TEST(NumericalIntegrationTest, ZeroRKDP) {
+  frc::Vectord<1> y1 = frc::RKDP(
+      [](const frc::Vectord<1>& x, const frc::Vectord<1>& u) {
+        return frc::Vectord<1>::Zero();
+      },
+      frc::Vectord<1>{0.0}, frc::Vectord<1>{0.0}, 0.1_s);
+  EXPECT_NEAR(y1(0), 0.0, 1e-3);
+}
+
 // Tests that integrating dx/dt = e^x works with RKDP
 TEST(NumericalIntegrationTest, ExponentialRKDP) {
   frc::Vectord<1> y0{0.0};