diff --git a/app-proto/src/assembly.rs b/app-proto/src/assembly.rs
index 9b0e065..28afb19 100644
--- a/app-proto/src/assembly.rs
+++ b/app-proto/src/assembly.rs
@@ -371,8 +371,8 @@ impl Assembly {
             }
         }
         
-        // step each element along the mass shell geodesic that matches its
-        // velocity in the deformation found above
+        // step the assembly along the deformation, and then project each
+        // element back onto its mass shall
         /* KLUDGE */
         // since our test assemblies only include spheres, we assume that every
         // element is on the 1 mass shell
@@ -380,9 +380,25 @@ impl Assembly {
             elt.representation.update_silent(|rep| {
                 match elt.column_index {
                     Some(column_index) => {
+                        // apply the deformation linearly
                         let rep_next = &*rep + motion_proj.column(column_index);
-                        let normalizer = rep_next.dot(&(&*Q * &rep_next));
-                        rep.set_column(0, &(rep_next / normalizer));
+                        
+                        // project back onto the mass shell by contracting
+                        // toward the last coordinate axis
+                        let q_sp = rep_next.fixed_rows::<3>(0).norm_squared();
+                        let half_q_lt = -2.0 * rep_next[3] * rep_next[4];
+                        let half_q_lt_sq = half_q_lt * half_q_lt;
+                        let scaling = half_q_lt + (q_sp + half_q_lt_sq).sqrt();
+                        rep.fixed_rows_mut::<4>(0).copy_from(
+                            &(rep_next.fixed_rows::<4>(0) / scaling)
+                        );
+                        rep[4] = rep_next[4];
+                        
+                        /* DEBUG */
+                        // report self-product before and after projection
+                        console::log_1(&JsValue::from(
+                            format!("Self-product of element representation\n  After step:    {}\n  Scaling:       {}\n  After scaling: {}", rep_next.dot(&(&*Q * &rep_next)), scaling, rep.dot(&(&*Q * &*rep)))
+                        ));
                     },
                     None => {
                         console::log_1(&JsValue::from(