diff --git a/app-proto/src/assembly.rs b/app-proto/src/assembly.rs
index 9b0e065..7073c9e 100644
--- a/app-proto/src/assembly.rs
+++ b/app-proto/src/assembly.rs
@@ -5,7 +5,7 @@ use std::{collections::BTreeSet, sync::atomic::{AtomicU64, Ordering}};
 use sycamore::prelude::*;
 use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */
 
-use crate::engine::{realize_gram, local_unif_to_std, ConfigSubspace, PartialMatrix, Q};
+use crate::engine::{realize_gram, local_unif_to_std, ConfigSubspace, PartialMatrix};
 
 // the types of the keys we use to access an assembly's elements and constraints
 pub type ElementKey = usize;
@@ -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. this changes the elements'
+        // normalizations, so we restore those afterward
         /* KLUDGE */
         // since our test assemblies only include spheres, we assume that every
         // element is on the 1 mass shell
@@ -380,9 +380,16 @@ impl Assembly {
             elt.representation.update_silent(|rep| {
                 match elt.column_index {
                     Some(column_index) => {
-                        let rep_next = &*rep + motion_proj.column(column_index);
-                        let normalizer = rep_next.dot(&(&*Q * &rep_next));
-                        rep.set_column(0, &(rep_next / normalizer));
+                        // step the assembly along the deformation
+                        *rep += motion_proj.column(column_index);
+                        
+                        // restore normalization by contracting toward the last
+                        // coordinate axis
+                        let q_sp = rep.fixed_rows::<3>(0).norm_squared();
+                        let half_q_lt = -2.0 * rep[3] * rep[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).scale_mut(1.0 / scaling);
                     },
                     None => {
                         console::log_1(&JsValue::from(