Integrate Refactor solver sources and dual MSVC CMake builds

tests/unit/elements/finite_rotation_test.cpp

@@ -161,6 +161,28 @@ TEST(FiniteRotation, RejectsCoordinatesInsidePrincipalBranchMargin) {
             "invalid-accepted-state");
 }
 
+TEST(FiniteRotation, SpatialMomentSolvePreservesKnownLoadAndVirtualWork) {
+  const Vector3 moment{2.0, -3.0, 4.0};
+  const Vector3 variation{0.3, -0.5, 0.7};
+  const double pi = std::acos(-1.0);
+  for (const double angle : {0.0, 1e-9, 0.7, pi - 1e-6}) {
+    const double a = angle == 0.0 ? 1.0 : std::sin(angle) / angle;
+    const double b = angle < 1e-8 ? angle / 2.0 :
+        (1.0 - std::cos(angle)) / angle;
+    // Independent z-axis J^T*m; the axial component is unchanged.
+    const Vector3 generalized{a * moment.X() + b * moment.Y(),
+                              -b * moment.X() + a * moment.Y(), moment.Z()};
+    const auto solved = SpatialMomentSO3(Vector3{0, 0, angle}, generalized);
+    ASSERT_TRUE(solved.HasValue());
+    ExpectVectorNear(solved.Value(), moment, 1e-11);
+    const Vector3 spatial_variation{a * variation.X() - b * variation.Y(),
+                                    b * variation.X() + a * variation.Y(),
+                                    variation.Z()};
+    EXPECT_NEAR(generalized.Dot(variation),
+                solved.Value().Dot(spatial_variation), 1e-11);
+  }
+}
+
 TEST(FiniteRotation,
      JacobiansAreFiniteInverseTransposeAndDerivativeConsistent) {
   const double pi = std::acos(-1.0);
@@ -172,18 +194,13 @@ TEST(FiniteRotation,
 
   for (const Vector3& phi : rotations) {
     const Matrix left_jacobian = LeftJacobianSO3(phi);
-    const Matrix inverse_transpose = InverseTransposeLeftJacobianSO3(phi);
     EXPECT_TRUE(IsFinite(left_jacobian));
-    EXPECT_TRUE(IsFinite(inverse_transpose));
 
-    const Matrix identity =
-        Transpose(left_jacobian).Multiply(inverse_transpose);
-    for (std::size_t row = 0U; row < kRotationDimension; ++row) {
-      for (std::size_t column = 0U; column < kRotationDimension; ++column) {
-        EXPECT_NEAR(identity(row, column), row == column ? 1.0 : 0.0,
-                    1.0e-11);
-      }
-    }
+    const Vector3 load{0.7, -0.2, 0.4};
+    const auto spatial = SpatialMomentSO3(phi, load);
+    ASSERT_TRUE(spatial.HasValue());
+    ExpectVectorNear(Multiply(Transpose(left_jacobian), spatial.Value()),
+                     load, 1e-11);
 
     const Vector3 director = Multiply(ExpSkew(phi), Vector3{0.0, 0.0, 1.0});
     const Vector3 positive =