diff --git a/crates/bevy_xpbd_3d/snapshots/bevy_xpbd_3d__tests__cubes_simulation_is_deterministic_across_machines.snap b/crates/bevy_xpbd_3d/snapshots/bevy_xpbd_3d__tests__cubes_simulation_is_deterministic_across_machines.snap
index 71b08a86..164fba50 100644
--- a/crates/bevy_xpbd_3d/snapshots/bevy_xpbd_3d__tests__cubes_simulation_is_deterministic_across_machines.snap
+++ b/crates/bevy_xpbd_3d/snapshots/bevy_xpbd_3d__tests__cubes_simulation_is_deterministic_across_machines.snap
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@@ -837,15 +837,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                -2.1417034,
-                4.499789,
-                -4.267216,
+                -2.0943875,
+                4.4998355,
+                -4.623846,
             ),
             rotation: Quat(
-                6.6696986e-5,
-                0.025581645,
-                1.927695e-6,
-                0.9996727,
+                0.00010044623,
+                0.012530968,
+                -8.938792e-6,
+                0.9999215,
             ),
             scale: Vec3(
                 1.0,
@@ -860,15 +860,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                -2.026439,
-                4.4998703,
-                -2.0626712,
+                -2.009536,
+                4.499907,
+                -2.4300594,
             ),
             rotation: Quat(
-                7.409019e-6,
-                0.010577596,
-                -9.2272785e-6,
-                0.99994403,
+                -2.0774619e-6,
+                0.014378485,
+                -5.443816e-6,
+                0.99989665,
             ),
             scale: Vec3(
                 1.0,
@@ -883,15 +883,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                -2.1309397,
-                4.4999185,
-                0.07222076,
+                -1.9585384,
+                4.499923,
+                -0.22404596,
             ),
             rotation: Quat(
-                1.1899338e-6,
-                -0.00022890558,
-                -7.676071e-6,
-                1.0,
+                1.715594e-5,
+                0.014164529,
+                -3.7965892e-5,
+                0.9998997,
             ),
             scale: Vec3(
                 1.0,
@@ -906,15 +906,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                -2.0055707,
-                4.4998903,
-                2.5978162,
+                -1.8411386,
+                4.4998856,
+                2.3135095,
             ),
             rotation: Quat(
-                9.862658e-6,
-                0.03825622,
-                6.371329e-6,
-                0.99926794,
+                -3.3378979e-6,
+                -0.056289833,
+                1.8587364e-6,
+                0.99841446,
             ),
             scale: Vec3(
                 1.0,
@@ -929,15 +929,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                0.20182578,
-                4.4999266,
-                -4.6506033,
+                -0.02375713,
+                4.4996953,
+                -4.2030654,
             ),
             rotation: Quat(
-                -3.3825906e-6,
-                0.04204805,
-                -4.324491e-6,
-                0.9991156,
+                0.00011672663,
+                0.03757818,
+                -1.2387409e-5,
+                0.9992937,
             ),
             scale: Vec3(
                 1.0,
@@ -952,15 +952,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                0.06143783,
-                4.4999104,
-                -2.1186182,
+                0.119919084,
+                4.4998827,
+                -2.0700102,
             ),
             rotation: Quat(
-                9.198389e-6,
-                0.057064958,
-                -1.6621138e-5,
-                0.99837047,
+                4.0283912e-6,
+                0.05287602,
+                -5.329639e-6,
+                0.9986011,
             ),
             scale: Vec3(
                 1.0,
@@ -975,15 +975,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                0.09008749,
-                4.499909,
-                0.4059078,
+                0.19294138,
+                4.499873,
+                0.22602274,
             ),
             rotation: Quat(
-                -1.3736032e-5,
-                -0.04082854,
-                1.8841715e-6,
-                0.9991662,
+                2.7269325e-6,
+                0.010626739,
+                -1.257475e-5,
+                0.99994355,
             ),
             scale: Vec3(
                 1.0,
@@ -998,15 +998,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                0.10141875,
-                4.499917,
-                2.4459357,
+                0.31366748,
+                4.4999237,
+                2.7180665,
             ),
             rotation: Quat(
-                2.1650978e-5,
-                -0.02168258,
-                5.229496e-6,
-                0.9997649,
+                5.3005783e-6,
+                -0.06315649,
+                -1.3187989e-5,
+                0.99800366,
             ),
             scale: Vec3(
                 1.0,
@@ -1021,15 +1021,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                2.4117937,
-                4.4998984,
-                -4.3657637,
+                2.377476,
+                4.4999547,
+                -4.8546257,
             ),
             rotation: Quat(
-                -4.2042775e-6,
-                0.048985492,
-                -6.035323e-6,
-                0.9987995,
+                2.7817585e-5,
+                0.17257857,
+                -1.4667208e-5,
+                0.9849958,
             ),
             scale: Vec3(
                 1.0,
@@ -1044,15 +1044,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                2.2275023,
-                4.499888,
-                -1.8621465,
+                2.314021,
+                4.499904,
+                -2.3202064,
             ),
             rotation: Quat(
-                1.0838617e-5,
-                0.03107816,
-                2.556269e-6,
-                0.99951696,
+                -1.2845678e-5,
+                0.01641865,
+                -3.9993383e-6,
+                0.99986523,
             ),
             scale: Vec3(
                 1.0,
@@ -1067,15 +1067,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                2.3308487,
-                4.49984,
-                0.22742787,
+                2.4601562,
+                4.499923,
+                0.03035463,
             ),
             rotation: Quat(
-                5.771548e-6,
-                0.029534405,
-                2.5869722e-6,
-                0.99956375,
+                -1.0146865e-5,
+                0.042424247,
+                9.197388e-8,
+                0.9990997,
             ),
             scale: Vec3(
                 1.0,
@@ -1090,15 +1090,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                2.3696156,
-                4.4998636,
-                2.8025134,
+                2.5232496,
+                4.499871,
+                2.199358,
             ),
             rotation: Quat(
-                1.5080648e-5,
-                -0.07724971,
-                -2.596575e-5,
-                0.9970118,
+                1.0287707e-5,
+                0.027183056,
+                -1.0482277e-5,
+                0.99963045,
             ),
             scale: Vec3(
                 1.0,
@@ -1113,15 +1113,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                -4.5051923,
-                6.4998903,
-                -3.810133,
+                -4.798367,
+                6.499823,
+                -4.896724,
             ),
             rotation: Quat(
-                4.203818e-6,
-                0.00550233,
-                -4.8972784e-6,
-                0.99998486,
+                4.156623e-5,
+                -0.18305051,
+                -4.9355835e-6,
+                0.9831035,
             ),
             scale: Vec3(
                 1.0,
@@ -1136,15 +1136,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                -4.5689893,
-                6.499893,
-                -1.5330108,
+                -13.893423,
+                0.49999946,
+                -3.619525,
             ),
             rotation: Quat(
-                -1.2279531e-5,
-                -0.07520555,
-                7.7855987e-7,
-                0.99716806,
+                -0.51768076,
+                -0.517681,
+                0.48167115,
+                0.48166996,
             ),
             scale: Vec3(
                 1.0,
@@ -1159,15 +1159,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                -4.7065063,
-                6.4998336,
-                0.5526104,
+                -4.381537,
+                6.4999037,
+                0.48308283,
             ),
             rotation: Quat(
-                1.4557541e-5,
-                -0.03367962,
-                -8.779749e-6,
-                0.9994327,
+                -9.016728e-6,
+                -0.07982172,
+                -8.499087e-6,
+                0.9968092,
             ),
             scale: Vec3(
                 1.0,
@@ -1182,15 +1182,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                -4.6731706,
-                6.499872,
-                2.622469,
+                -8.318473,
+                0.49999946,
+                19.172176,
             ),
             rotation: Quat(
-                1.1933248e-5,
-                -0.0046023433,
-                -7.500923e-6,
-                0.9999894,
+                0.6616829,
+                -0.24935219,
+                0.24935146,
+                0.66168195,
             ),
             scale: Vec3(
                 1.0,
@@ -1205,15 +1205,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                -2.1444836,
-                6.499803,
-                -4.349761,
+                -2.1034138,
+                6.4998574,
+                -4.8453918,
             ),
             rotation: Quat(
-                6.1202765e-5,
-                0.0016883515,
-                -1.1926737e-6,
-                0.99999857,
+                9.41463e-5,
+                0.0820297,
+                6.9586326e-6,
+                0.9966299,
             ),
             scale: Vec3(
                 1.0,
@@ -1228,15 +1228,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                -2.1940129,
-                6.4998727,
-                -2.1784127,
+                -1.9645659,
+                6.49991,
+                -2.2860827,
             ),
             rotation: Quat(
-                1.1310669e-5,
-                -0.019140596,
-                -1.1338596e-5,
-                0.9998168,
+                -1.9683644e-6,
+                -0.021907628,
+                -3.0639426e-6,
+                0.99976,
             ),
             scale: Vec3(
                 1.0,
@@ -1251,15 +1251,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                -2.153471,
-                6.499916,
-                -0.13986145,
+                -1.9352555,
+                6.4999294,
+                -0.2553877,
             ),
             rotation: Quat(
-                5.362298e-6,
-                -0.011965028,
-                -9.501719e-6,
-                0.9999284,
+                1.7038174e-5,
+                -0.035811152,
+                -4.1647163e-5,
+                0.9993586,
             ),
             scale: Vec3(
                 1.0,
@@ -1274,15 +1274,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                -2.0463588,
-                6.499861,
-                2.3378937,
+                -1.949988,
+                6.4998813,
+                2.0137444,
             ),
             rotation: Quat(
-                4.03701e-6,
-                0.013133474,
-                5.30854e-6,
-                0.99991375,
+                4.7868593e-7,
+                -0.004052656,
+                -2.5726246e-8,
+                0.9999918,
             ),
             scale: Vec3(
                 1.0,
@@ -1297,15 +1297,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                0.45179436,
-                6.499898,
-                -5.082483,
+                0.08226854,
+                6.4997396,
+                -4.4143085,
             ),
             rotation: Quat(
-                -7.7595705e-6,
-                0.23150676,
-                2.7409362e-6,
-                0.9728333,
+                0.000111104484,
+                -0.022358429,
+                -2.2984656e-5,
+                0.99975,
             ),
             scale: Vec3(
                 1.0,
@@ -1320,15 +1320,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                -0.04225794,
-                6.4999123,
-                -2.307129,
+                0.043099843,
+                6.49989,
+                -2.2432802,
             ),
             rotation: Quat(
-                1.1916372e-5,
-                0.018675506,
-                -1.88421e-5,
-                0.9998256,
+                -4.881092e-7,
+                -0.017938888,
+                -5.358564e-6,
+                0.99983907,
             ),
             scale: Vec3(
                 1.0,
@@ -1343,15 +1343,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                0.08154735,
-                6.4999113,
-                0.37454426,
+                0.20691219,
+                6.499881,
+                0.23858999,
             ),
             rotation: Quat(
-                -1.4968491e-5,
-                -0.0477015,
-                1.3139173e-6,
-                0.9988616,
+                3.7870827e-6,
+                -0.06124742,
+                -1.658932e-5,
+                0.99812263,
             ),
             scale: Vec3(
                 1.0,
@@ -1366,15 +1366,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                0.14312406,
-                6.4999194,
-                2.393739,
+                0.15775675,
+                6.499881,
+                3.053992,
             ),
             rotation: Quat(
-                1.992816e-5,
-                -0.045010325,
-                3.2358441e-6,
-                0.99898654,
+                7.822202e-6,
+                -0.11158954,
+                -1.5739672e-5,
+                0.9937544,
             ),
             scale: Vec3(
                 1.0,
@@ -1389,15 +1389,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                2.8398702,
-                6.499892,
-                -4.350771,
+                2.31714,
+                6.499921,
+                -4.240581,
             ),
             rotation: Quat(
-                1.3100966e-6,
-                0.06222463,
-                -1.1506304e-5,
-                0.9980622,
+                1.8280816e-5,
+                0.020745432,
+                -6.7741507e-6,
+                0.99978477,
             ),
             scale: Vec3(
                 1.0,
@@ -1412,15 +1412,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                2.064684,
-                6.499893,
-                -2.0412836,
+                2.0382423,
+                6.4999146,
+                -2.0699782,
             ),
             rotation: Quat(
-                1.0947143e-5,
-                0.05536288,
-                1.9659664e-7,
-                0.9984663,
+                -1.1182783e-5,
+                -0.017901609,
+                -5.2746063e-6,
+                0.9998398,
             ),
             scale: Vec3(
                 1.0,
@@ -1435,15 +1435,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                2.2600605,
-                6.499847,
-                0.10657572,
+                2.3031816,
+                6.499888,
+                -0.0062856125,
             ),
             rotation: Quat(
-                1.1522514e-5,
-                0.027097696,
-                9.932345e-7,
-                0.9996328,
+                -1.2922834e-5,
+                -0.0152022885,
+                5.0969556e-6,
+                0.9998844,
             ),
             scale: Vec3(
                 1.0,
@@ -1458,15 +1458,15 @@ expression: bodies
         ),
         Transform {
             translation: Vec3(
-                2.5827608,
-                6.4998703,
-                2.3985717,
+                2.482787,
+                6.4998736,
+                2.4378264,
             ),
             rotation: Quat(
-                1.895812e-5,
-                0.048459783,
-                -2.5742962e-5,
-                0.99882513,
+                7.338764e-6,
+                -0.144237,
+                -1.5116398e-5,
+                0.9895432,
             ),
             scale: Vec3(
                 1.0,
diff --git a/src/constraints/angular_constraint.rs b/src/constraints/angular_constraint.rs
index a37c355a..940527f4 100644
--- a/src/constraints/angular_constraint.rs
+++ b/src/constraints/angular_constraint.rs
@@ -67,9 +67,18 @@ pub trait AngularConstraint: XpbdConstraint<2> {
         // Apply rotational updates
         if body1.rb.is_dynamic() {
             *body1.rotation += Self::get_delta_rot(rot1, inv_inertia1, p);
+
+            // In 3D, subtracting quaternions like above can result in unnormalized rotations,
+            // which causes stability issues (see #235) and panics when trying to rotate unit vectors.
+            // TODO: It would be nice to avoid normalization if possible.
+            //       Maybe the math above can be done in a way that keeps rotations normalized?
+            body1.rotation.0 = body1.rotation.0.normalize();
         }
         if body2.rb.is_dynamic() {
             *body2.rotation -= Self::get_delta_rot(rot2, inv_inertia2, p);
+
+            // See comments for `body1` above.
+            body2.rotation.0 = body2.rotation.0.normalize();
         }
 
         p
diff --git a/src/constraints/position_constraint.rs b/src/constraints/position_constraint.rs
index 1740654e..b3ae7a62 100644
--- a/src/constraints/position_constraint.rs
+++ b/src/constraints/position_constraint.rs
@@ -34,10 +34,25 @@ pub trait PositionConstraint: XpbdConstraint<2> {
         if body1.rb.is_dynamic() && body1.dominance() <= body2.dominance() {
             body1.accumulated_translation.0 += p * inv_mass1;
             *body1.rotation += Self::get_delta_rot(rot1, inv_inertia1, r1, p);
+
+            #[cfg(feature = "3d")]
+            {
+                // In 3D, subtracting quaternions like above can result in unnormalized rotations,
+                // which causes stability issues (see #235) and panics when trying to rotate unit vectors.
+                // TODO: It would be nice to avoid normalization if possible.
+                //       Maybe the math above can be done in a way that keeps rotations normalized?
+                body1.rotation.0 = body1.rotation.0.normalize();
+            }
         }
         if body2.rb.is_dynamic() && body2.dominance() <= body1.dominance() {
             body2.accumulated_translation.0 -= p * inv_mass2;
             *body2.rotation -= Self::get_delta_rot(rot2, inv_inertia2, r2, p);
+
+            #[cfg(feature = "3d")]
+            {
+                // See comments for `body1` above.
+                body2.rotation.0 = body2.rotation.0.normalize();
+            }
         }
 
         p