diff --git a/src/forces.zig b/src/forces.zig
index ca3ee49..86171ea 100644
--- a/src/forces.zig
+++ b/src/forces.zig
@@ -34,9 +34,9 @@ pub fn drag(
     velocity: vec3.Vec3F64,
 ) vec3.Vec3F64 {
     return .init(
-        -velocity.x() * drag_coefficient,
-        -velocity.y() * drag_coefficient,
-        -velocity.z() * drag_coefficient,
+        velocity.x() * drag_coefficient,
+        velocity.y() * drag_coefficient,
+        velocity.z() * drag_coefficient,
     );
 }
 
@@ -73,7 +73,7 @@ test "drag is correct" {
     const velocity = vec3.Vec3F64.init(0, 1, 1);
     const f_drag = drag(0.5, velocity);
 
-    try std.testing.expectApproxEqAbs(-0.0, f_drag.x(), 1e-11);
-    try std.testing.expectApproxEqAbs(-0.5, f_drag.y(), 1e-11);
-    try std.testing.expectApproxEqAbs(-0.5, f_drag.z(), 1e-11);
+    try std.testing.expectApproxEqAbs(0, f_drag.x(), 1e-11);
+    try std.testing.expectApproxEqAbs(0.5, f_drag.y(), 1e-11);
+    try std.testing.expectApproxEqAbs(0.5, f_drag.z(), 1e-11);
 }
diff --git a/src/integration.zig b/src/integration.zig
index b6d53cd..1e7578c 100644
--- a/src/integration.zig
+++ b/src/integration.zig
@@ -28,14 +28,14 @@ pub fn timestep(dt: f64, d: drone.Drone, props: []const drone.Propeller, s: *dro
     );
 
     s.omega = vec3.vec3Add(s.omega, vec3.vec3Scale(omega_dot, dt));
-    const half_omega_quat: vec3.QuatF64 = .init(
+    const half_omege_quat: vec3.QuatF64 = .init(
         s.omega.x() * 0.5,
         s.omega.y() * 0.5,
         s.omega.z() * 0.5,
         0,
     );
 
-    const qdot = vec3.quatMul(half_omega_quat, s.q);
+    const qdot = vec3.quatMul(half_omege_quat, s.q);
     s.q = vec3.quatAdd(s.q, vec3.quatScale(qdot, dt)).normalized();
     return;
 }
@@ -85,23 +85,4 @@ test "Validate timesteps" {
     try std.testing.expectApproxEqAbs(0.12403234937465502, state.q.y(), 1e-12);
     try std.testing.expectApproxEqAbs(0.006201617468732751, state.q.z(), 1e-11);
     try std.testing.expectApproxEqAbs(0.9922587949972401, state.q.w(), 1e-11);
-
-    timestep(0.005, d, &props, &state);
-
-    try std.testing.expectApproxEqAbs(-1.23072190e+01, state.v.x(), 1e-7);
-    try std.testing.expectApproxEqAbs(-7.69201185e-02, state.v.y(), 1e-8);
-    try std.testing.expectApproxEqAbs(-9.83635311e+01, state.v.z(), 1e-7);
-
-    try std.testing.expectApproxEqAbs(-6.15360950e-02, state.x_cg.x(), 1e-9);
-    try std.testing.expectApproxEqAbs(-3.84600592e-04, state.x_cg.y(), 1e-9);
-    try std.testing.expectApproxEqAbs(-7.41572489e-01, state.x_cg.z(), 1e-9);
-
-    try std.testing.expectApproxEqAbs(-0.46875, state.omega.x(), 1e-12);
-    try std.testing.expectApproxEqAbs(100, state.omega.y(), 1e-12);
-    try std.testing.expectApproxEqAbs(5, state.omega.z(), 1e-11);
-
-    try std.testing.expectApproxEqAbs(-0.0011280012096230429, state.q.x(), 1e-12);
-    try std.testing.expectApproxEqAbs(0.36096743708693396, state.q.y(), 1e-12);
-    try std.testing.expectApproxEqAbs(0.01790701920276581, state.q.z(), 1e-12);
-    try std.testing.expectApproxEqAbs(0.9324057998744074, state.q.w(), 1e-12);
 }
diff --git a/src/vec3.zig b/src/vec3.zig
index 3079253..e9cdd25 100644
--- a/src/vec3.zig
+++ b/src/vec3.zig
@@ -90,7 +90,7 @@ pub fn mat3Mul(a: Mat3F64, b: Mat3F64) Mat3F64 {
 pub fn mat3Det(a: Mat3F64) f64 {
     return a.row1.x() * (a.row2.y() * a.row3.z() - a.row2.z() * a.row3.y()) -
         a.row1.y() * (a.row2.x() * a.row3.z() - a.row2.z() * a.row3.x()) +
-        a.row1.z() * (a.row2.x() * a.row3.y() - a.row2.y() * a.row3.x());
+        a.row1.y() * (a.row2.x() * a.row3.y() - a.row2.y() * a.row3.x());
 }
 
 pub fn mat3Inv(a: Mat3F64) Mat3F64 {
@@ -105,7 +105,7 @@ pub fn mat3Inv(a: Mat3F64) Mat3F64 {
     );
     const row2 = vec3Scale(
         .init(
-            a.row2.z() * a.row3.x() - a.row2.x() * a.row3.z(),
+            a.row2.z() * a.row3.x() + a.row2.x() * a.row3.z(),
             a.row1.x() * a.row3.z() - a.row1.z() * a.row3.x(),
             a.row1.z() * a.row2.x() - a.row1.x() * a.row2.z(),
         ),
@@ -113,7 +113,7 @@ pub fn mat3Inv(a: Mat3F64) Mat3F64 {
     );
     const row3 = vec3Scale(
         .init(
-            a.row2.x() * a.row3.y() - a.row2.y() * a.row3.x(),
+            a.row2.x() * a.row3.y() + a.row2.y() * a.row3.x(),
             a.row1.y() * a.row3.x() - a.row1.x() * a.row3.y(),
             a.row1.x() * a.row2.y() - a.row1.y() * a.row2.x(),
         ),
@@ -321,30 +321,30 @@ test "Mat3 mul works" {
 test "mat determinant works" {
     const a: Mat3F64 = .{
         .row1 = Vec3F64.init(1, 2, 3),
-        .row2 = Vec3F64.init(4, 1, 5),
-        .row3 = Vec3F64.init(3, 1, 9),
+        .row2 = Vec3F64.init(0, 1, 5),
+        .row3 = Vec3F64.init(0, 0, 9),
     };
-    try std.testing.expectApproxEqAbs(-35, mat3Det(a), 1e-12);
+    try std.testing.expectApproxEqAbs(9, mat3Det(a), 1e-12);
 }
 
 test "mat inverse works" {
     const a: Mat3F64 = .{
         .row1 = Vec3F64.init(1, 2, 3),
-        .row2 = Vec3F64.init(4, 1, 5),
-        .row3 = Vec3F64.init(3, 1, 9),
+        .row2 = Vec3F64.init(0, 1, 5),
+        .row3 = Vec3F64.init(0, 0, 9),
     };
 
     const ainv = mat3Inv(a);
 
-    try std.testing.expectApproxEqAbs(-4.0 / 35.0, ainv.row1.x(), 1e-12);
-    try std.testing.expectApproxEqAbs(3.0 / 7.0, ainv.row1.y(), 1e-12);
-    try std.testing.expectApproxEqAbs(-1.0 / 5.0, ainv.row1.z(), 1e-12);
-    try std.testing.expectApproxEqAbs(3.0 / 5.0, ainv.row2.x(), 1e-12);
-    try std.testing.expectApproxEqAbs(0, ainv.row2.y(), 1e-12);
-    try std.testing.expectApproxEqAbs(-1.0 / 5.0, ainv.row2.z(), 1e-12);
-    try std.testing.expectApproxEqAbs(-1.0 / 35.0, ainv.row3.x(), 1e-12);
-    try std.testing.expectApproxEqAbs(-1.0 / 7.0, ainv.row3.y(), 1e-12);
-    try std.testing.expectApproxEqAbs(1.0 / 5.0, ainv.row3.z(), 1e-12);
+    try std.testing.expectApproxEqAbs(1, ainv.row1.x(), 1e-12);
+    try std.testing.expectApproxEqAbs(-2, ainv.row1.y(), 1e-12);
+    try std.testing.expectApproxEqAbs(7.0 / 9.0, ainv.row1.z(), 1e-12);
+    try std.testing.expectApproxEqAbs(0, ainv.row2.x(), 1e-12);
+    try std.testing.expectApproxEqAbs(1, ainv.row2.y(), 1e-12);
+    try std.testing.expectApproxEqAbs(-5.0 / 9.0, ainv.row2.z(), 1e-12);
+    try std.testing.expectApproxEqAbs(0, ainv.row3.x(), 1e-12);
+    try std.testing.expectApproxEqAbs(0, ainv.row3.y(), 1e-12);
+    try std.testing.expectApproxEqAbs(1.0 / 9.0, ainv.row3.z(), 1e-12);
 }
 test "vec3 mul mat3 works" {
     const b: Mat3F64 = .{