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style(docs): use American English spelling per STYLEGUIDE #2586

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8 changes: 4 additions & 4 deletions python/LQR.ipynb
Original file line number Diff line number Diff line change
Expand Up @@ -298,7 +298,7 @@
"source": [
"## Stable standing on one leg\n",
"\n",
"Clearly this initial pose is not stable. We'll try to find a stabilising control law using a [Linear Quadratic Regulator](https://en.wikipedia.org/wiki/Linear%E2%80%93quadratic_regulator)."
"Clearly this initial pose is not stable. We'll try to find a stabilizing control law using a [Linear Quadratic Regulator](https://en.wikipedia.org/wiki/Linear%E2%80%93quadratic_regulator)."
]
},
{
Expand Down Expand Up @@ -358,7 +358,7 @@
"A = \\frac{\\partial f}{\\partial x} \\quad\n",
"B = \\frac{\\partial f}{\\partial u}\n",
"$$\n",
"In order to perform the linearization, we need to choose some setpoints $x$ and $u$ around which we will linearize. We already know $x$, this is our initial pose of standing on one leg. But what about $u$? How do we find the \"best\" control around which to linearise?\n",
"In order to perform the linearization, we need to choose some setpoints $x$ and $u$ around which we will linearize. We already know $x$, this is our initial pose of standing on one leg. But what about $u$? How do we find the \"best\" control around which to linearize?\n",
"\n",
"The answer is inverse dynamics."
]
Expand Down Expand Up @@ -786,7 +786,7 @@
"source": [
"### Stable standing\n",
"\n",
"We can now try our stabilising controller.\n",
"We can now try our stabilizing controller.\n",
"\n",
"Note that in order to apply our gain matrix $K$, we need to use `mj_differentiatePos` which computes the difference of two positions. This is important because the root orientation is given by a length-4 quaternion, while the difference of two quaternions (in the tangent space) is length-3. In MuJoCo notation, positions (`qpos`) are of size `nq` while a position differences (and velocities) are of size `nv`.\n"
]
Expand Down Expand Up @@ -867,7 +867,7 @@
"mujoco.mjv_defaultFreeCamera(model, camera)\n",
"camera.distance = 2.3\n",
"\n",
"# Enable contact force visualisation.\n",
"# Enable contact force visualization.\n",
"scene_option = mujoco.MjvOption()\n",
"scene_option.flags[mujoco.mjtVisFlag.mjVIS_CONTACTFORCE] = True\n",
"\n",
Expand Down