diff --git a/wpimath/src/main/java/edu/wpi/first/math/geometry/CoordinateAxis.java b/wpimath/src/main/java/edu/wpi/first/math/geometry/CoordinateAxis.java
index 19f4a3f083..889ac35419 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/geometry/CoordinateAxis.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/geometry/CoordinateAxis.java
@@ -10,6 +10,13 @@ import edu.wpi.first.math.numbers.N3;
 
 /** A class representing a coordinate system axis within the NWU coordinate system. */
 public class CoordinateAxis {
+  private static final CoordinateAxis m_n = new CoordinateAxis(1.0, 0.0, 0.0);
+  private static final CoordinateAxis m_s = new CoordinateAxis(-1.0, 0.0, 0.0);
+  private static final CoordinateAxis m_e = new CoordinateAxis(0.0, -1.0, 0.0);
+  private static final CoordinateAxis m_w = new CoordinateAxis(0.0, 1.0, 0.0);
+  private static final CoordinateAxis m_u = new CoordinateAxis(0.0, 0.0, 1.0);
+  private static final CoordinateAxis m_d = new CoordinateAxis(0.0, 0.0, -1.0);
+
   final Vector<N3> m_axis;
 
   /**
@@ -31,7 +38,7 @@ public class CoordinateAxis {
    */
   @SuppressWarnings("MethodName")
   public static CoordinateAxis N() {
-    return new CoordinateAxis(1.0, 0.0, 0.0);
+    return m_n;
   }
 
   /**
@@ -41,7 +48,7 @@ public class CoordinateAxis {
    */
   @SuppressWarnings("MethodName")
   public static CoordinateAxis S() {
-    return new CoordinateAxis(-1.0, 0.0, 0.0);
+    return m_s;
   }
 
   /**
@@ -51,7 +58,7 @@ public class CoordinateAxis {
    */
   @SuppressWarnings("MethodName")
   public static CoordinateAxis E() {
-    return new CoordinateAxis(0.0, -1.0, 0.0);
+    return m_e;
   }
 
   /**
@@ -61,7 +68,7 @@ public class CoordinateAxis {
    */
   @SuppressWarnings("MethodName")
   public static CoordinateAxis W() {
-    return new CoordinateAxis(0.0, 1.0, 0.0);
+    return m_w;
   }
 
   /**
@@ -71,7 +78,7 @@ public class CoordinateAxis {
    */
   @SuppressWarnings("MethodName")
   public static CoordinateAxis U() {
-    return new CoordinateAxis(0.0, 0.0, 1.0);
+    return m_u;
   }
 
   /**
@@ -81,6 +88,6 @@ public class CoordinateAxis {
    */
   @SuppressWarnings("MethodName")
   public static CoordinateAxis D() {
-    return new CoordinateAxis(0.0, 0.0, -1.0);
+    return m_d;
   }
 }
diff --git a/wpimath/src/main/java/edu/wpi/first/math/geometry/CoordinateSystem.java b/wpimath/src/main/java/edu/wpi/first/math/geometry/CoordinateSystem.java
index dae9eb8d84..449ba7438e 100644
--- a/wpimath/src/main/java/edu/wpi/first/math/geometry/CoordinateSystem.java
+++ b/wpimath/src/main/java/edu/wpi/first/math/geometry/CoordinateSystem.java
@@ -9,6 +9,13 @@ import edu.wpi.first.math.Nat;
 
 /** A helper class that converts Pose3d objects between different standard coordinate frames. */
 public class CoordinateSystem {
+  private static final CoordinateSystem m_nwu =
+      new CoordinateSystem(CoordinateAxis.N(), CoordinateAxis.W(), CoordinateAxis.U());
+  private static final CoordinateSystem m_edn =
+      new CoordinateSystem(CoordinateAxis.E(), CoordinateAxis.D(), CoordinateAxis.N());
+  private static final CoordinateSystem m_ned =
+      new CoordinateSystem(CoordinateAxis.N(), CoordinateAxis.E(), CoordinateAxis.D());
+
   // Rotation from this coordinate system to NWU coordinate system
   private final Rotation3d m_rotation;
 
@@ -86,7 +93,7 @@ public class CoordinateSystem {
    */
   @SuppressWarnings("MethodName")
   public static CoordinateSystem NWU() {
-    return new CoordinateSystem(CoordinateAxis.N(), CoordinateAxis.W(), CoordinateAxis.U());
+    return m_nwu;
   }
 
   /**
@@ -98,7 +105,7 @@ public class CoordinateSystem {
    */
   @SuppressWarnings("MethodName")
   public static CoordinateSystem EDN() {
-    return new CoordinateSystem(CoordinateAxis.E(), CoordinateAxis.D(), CoordinateAxis.N());
+    return m_edn;
   }
 
   /**
@@ -110,7 +117,7 @@ public class CoordinateSystem {
    */
   @SuppressWarnings("MethodName")
   public static CoordinateSystem NED() {
-    return new CoordinateSystem(CoordinateAxis.N(), CoordinateAxis.E(), CoordinateAxis.D());
+    return m_ned;
   }
 
   /**
diff --git a/wpimath/src/main/native/cpp/geometry/CoordinateAxis.cpp b/wpimath/src/main/native/cpp/geometry/CoordinateAxis.cpp
index b180b3c7ba..1d9c42a2a4 100644
--- a/wpimath/src/main/native/cpp/geometry/CoordinateAxis.cpp
+++ b/wpimath/src/main/native/cpp/geometry/CoordinateAxis.cpp
@@ -10,26 +10,32 @@ CoordinateAxis::CoordinateAxis(double x, double y, double z) : m_axis{x, y, z} {
   m_axis /= m_axis.norm();
 }
 
-CoordinateAxis CoordinateAxis::N() {
-  return CoordinateAxis{1.0, 0.0, 0.0};
+const CoordinateAxis& CoordinateAxis::N() {
+  static const CoordinateAxis instance{1.0, 0.0, 0.0};
+  return instance;
 }
 
-CoordinateAxis CoordinateAxis::S() {
-  return CoordinateAxis{-1.0, 0.0, 0.0};
+const CoordinateAxis& CoordinateAxis::S() {
+  static const CoordinateAxis instance{-1.0, 0.0, 0.0};
+  return instance;
 }
 
-CoordinateAxis CoordinateAxis::E() {
-  return CoordinateAxis{0.0, -1.0, 0.0};
+const CoordinateAxis& CoordinateAxis::E() {
+  static const CoordinateAxis instance{0.0, -1.0, 0.0};
+  return instance;
 }
 
-CoordinateAxis CoordinateAxis::W() {
-  return CoordinateAxis{0.0, 1.0, 0.0};
+const CoordinateAxis& CoordinateAxis::W() {
+  static const CoordinateAxis instance{0.0, 1.0, 0.0};
+  return instance;
 }
 
-CoordinateAxis CoordinateAxis::U() {
-  return CoordinateAxis{0.0, 0.0, 1.0};
+const CoordinateAxis& CoordinateAxis::U() {
+  static const CoordinateAxis instance{0.0, 0.0, 1.0};
+  return instance;
 }
 
-CoordinateAxis CoordinateAxis::D() {
-  return CoordinateAxis{0.0, 0.0, -1.0};
+const CoordinateAxis& CoordinateAxis::D() {
+  static const CoordinateAxis instance{0.0, 0.0, -1.0};
+  return instance;
 }
diff --git a/wpimath/src/main/native/cpp/geometry/CoordinateSystem.cpp b/wpimath/src/main/native/cpp/geometry/CoordinateSystem.cpp
index c05f927d4c..f4d200c92e 100644
--- a/wpimath/src/main/native/cpp/geometry/CoordinateSystem.cpp
+++ b/wpimath/src/main/native/cpp/geometry/CoordinateSystem.cpp
@@ -69,19 +69,22 @@ CoordinateSystem::CoordinateSystem(const CoordinateAxis& positiveX,
   m_rotation = Rotation3d{Quaternion{w, x, y, z}};
 }
 
-CoordinateSystem CoordinateSystem::NWU() {
-  return CoordinateSystem{CoordinateAxis::N(), CoordinateAxis::W(),
-                          CoordinateAxis::U()};
+const CoordinateSystem& CoordinateSystem::NWU() {
+  static const CoordinateSystem instance{
+      CoordinateAxis::N(), CoordinateAxis::W(), CoordinateAxis::U()};
+  return instance;
 }
 
-CoordinateSystem CoordinateSystem::EDN() {
-  return CoordinateSystem{CoordinateAxis::E(), CoordinateAxis::D(),
-                          CoordinateAxis::N()};
+const CoordinateSystem& CoordinateSystem::EDN() {
+  static const CoordinateSystem instance{
+      CoordinateAxis::E(), CoordinateAxis::D(), CoordinateAxis::N()};
+  return instance;
 }
 
-CoordinateSystem CoordinateSystem::NED() {
-  return CoordinateSystem{CoordinateAxis::N(), CoordinateAxis::E(),
-                          CoordinateAxis::D()};
+const CoordinateSystem& CoordinateSystem::NED() {
+  static const CoordinateSystem instance{
+      CoordinateAxis::N(), CoordinateAxis::E(), CoordinateAxis::D()};
+  return instance;
 }
 
 Pose3d CoordinateSystem::Convert(const Pose3d& pose,
diff --git a/wpimath/src/main/native/include/frc/geometry/CoordinateAxis.h b/wpimath/src/main/native/include/frc/geometry/CoordinateAxis.h
index 1ac1a2c07a..58b966ab07 100644
--- a/wpimath/src/main/native/include/frc/geometry/CoordinateAxis.h
+++ b/wpimath/src/main/native/include/frc/geometry/CoordinateAxis.h
@@ -37,32 +37,32 @@ class WPILIB_DLLEXPORT CoordinateAxis {
   /**
    * Returns a coordinate axis corresponding to +X in the NWU coordinate system.
    */
-  static CoordinateAxis N();
+  static const CoordinateAxis& N();
 
   /**
    * Returns a coordinate axis corresponding to -X in the NWU coordinate system.
    */
-  static CoordinateAxis S();
+  static const CoordinateAxis& S();
 
   /**
    * Returns a coordinate axis corresponding to -Y in the NWU coordinate system.
    */
-  static CoordinateAxis E();
+  static const CoordinateAxis& E();
 
   /**
    * Returns a coordinate axis corresponding to +Y in the NWU coordinate system.
    */
-  static CoordinateAxis W();
+  static const CoordinateAxis& W();
 
   /**
    * Returns a coordinate axis corresponding to +Z in the NWU coordinate system.
    */
-  static CoordinateAxis U();
+  static const CoordinateAxis& U();
 
   /**
    * Returns a coordinate axis corresponding to -Z in the NWU coordinate system.
    */
-  static CoordinateAxis D();
+  static const CoordinateAxis& D();
 
  private:
   friend class CoordinateSystem;
diff --git a/wpimath/src/main/native/include/frc/geometry/CoordinateSystem.h b/wpimath/src/main/native/include/frc/geometry/CoordinateSystem.h
index 8dd6a81f2f..1062aa5eae 100644
--- a/wpimath/src/main/native/include/frc/geometry/CoordinateSystem.h
+++ b/wpimath/src/main/native/include/frc/geometry/CoordinateSystem.h
@@ -42,21 +42,21 @@ class WPILIB_DLLEXPORT CoordinateSystem {
    *
    * The +X axis is north, the +Y axis is west, and the +Z axis is up.
    */
-  static CoordinateSystem NWU();
+  static const CoordinateSystem& NWU();
 
   /**
    * Returns an instance of the East-Down-North (EDN) coordinate system.
    *
    * The +X axis is east, the +Y axis is down, and the +Z axis is north.
    */
-  static CoordinateSystem EDN();
+  static const CoordinateSystem& EDN();
 
   /**
    * Returns an instance of the NED coordinate system.
    *
    * The +X axis is north, the +Y axis is east, and the +Z axis is down.
    */
-  static CoordinateSystem NED();
+  static const CoordinateSystem& NED();
 
   /**
    * Converts the given pose from one coordinate system to another.