Modded a bit more of the inertia lectures.

inertia/inertia-1.ipynb

@@ -218,10 +218,10 @@
    "source": [
     "#### Notation\n",
     "\n",
-    "$I^{P/O}_{ab}$ is the product of inertia of $P$ along two lines through point $O$ that are parallel to unit vectors $\\hat{n}_a$ and $\\hat{n}_b$.\n",
+    "$I^{P/O}_{ab}$ is the product of inertia of $P$ along two lines through point $O$ that are parallel to unit vectors $\\hat{\\bf n}_a$ and $\\hat{\\bf n}_b$.\n",
     "\n",
     "$$\n",
-    "I^{P/O}_{ab} \\triangleq m \\left( {\\mathbf p} \\times \\hat{n}_a \\right) \\cdot \\left( {\\mathbf p} \\times \\hat{n}_b \\right) \\tag{8.5}\n",
+    "I^{P/O}_{ab} \\triangleq m \\left( {\\mathbf p} \\times \\hat{\\bf n}_a \\right) \\cdot \\left( {\\mathbf p} \\times \\hat{\\bf n}_b \\right) \\tag{8.5}\n",
     "$$\n",
     "\n",
     "\n",
@@ -231,13 +231,13 @@
     "#### Product of inertia of system particles\n",
     "\n",
     "$$\n",
-    "I^{S/O}_{ab} \\triangleq \\sum_i m_i \\left( {\\mathbf p}_i \\times \\hat{n}_a \\right) \\cdot \\left( {\\mathbf p}_i \\times \\hat{n}_b \\right) \\tag{8.6}\n",
+    "I^{S/O}_{ab} \\triangleq \\sum_i m_i \\left( {\\mathbf p}_i \\times \\hat{\\bf n}_a \\right) \\cdot \\left( {\\mathbf p}_i \\times \\hat{\\bf n}_b \\right) \\tag{8.6}\n",
     "$$\n",
     "\n",
     "#### Product of inertia of continua\n",
     "\n",
     "$$\n",
-    "I^{B/O}_{ab} \\triangleq \\int \\mathrm{d}m \\left( {\\mathbf p} \\times \\hat{n}_a \\right) \\cdot \\left( {\\mathbf p} \\times \\hat{n}_b \\right) \\tag{8.7}\n",
+    "I^{B/O}_{ab} \\triangleq \\int \\mathrm{d}m \\left( {\\mathbf p} \\times \\hat{\\bf n}_a \\right) \\cdot \\left( {\\mathbf p} \\times \\hat{\\bf n}_b \\right) \\tag{8.7}\n",
     "$$\n",
     "\n",
     "```{figure} ./images/17.png\n",
@@ -272,16 +272,16 @@
     "\n",
     "#### Notation\n",
     "\n",
-    "$I^{P/O}_{aa}$ is the moment of inertia of P about a line through point $O$ which is parallel to the unit vector $\\hat{n}_a$.\n",
+    "$I^{P/O}_{aa}$ is the moment of inertia of P about a line through point $O$ which is parallel to the unit vector $\\hat{\\bf n}_a$.\n",
     "\n",
     "$$\n",
-    "I^{P/O}_{a} \\triangleq m \\left( {\\mathbf p} \\times \\hat{n}_a \\right) \\cdot \\left( {\\mathbf p} \\times \\hat{n}_a \\right) \\tag{8.8}\n",
+    "I^{P/O}_{a} \\triangleq m \\left( {\\mathbf p} \\times \\hat{\\bf n}_a \\right) \\cdot \\left( {\\mathbf p} \\times \\hat{\\bf n}_a \\right) \\tag{8.8}\n",
     "$$\n",
     "\n",
-    "$$ I^{P/O}_{aa} \\triangleq m \\cdot |{\\mathbf p} \\times \\hat{n}_a|^2$$\n",
+    "$$ I^{P/O}_{aa} \\triangleq m \\cdot |{\\mathbf p} \\times \\hat{\\bf n}_a|^2$$\n",
     "\n",
     "$$\n",
-    "= m \\left( |\\mathbf{p}| \\cdot |\\hat{n}_a| \\cdot \\sin\\theta \\right)^2\n",
+    "= m \\left( |\\mathbf{p}| \\cdot |\\hat{\\bf n}_a| \\cdot \\sin\\theta \\right)^2\n",
     "$$\n",
     "\n",
     "$$\n",
@@ -296,13 +296,13 @@
     "#### Moment of inertia of system of particles\n",
     "\n",
     "$$\n",
-    "I^{S/O}_{a} \\triangleq \\sum_i m_i \\left( {\\mathbf p}_i \\times \\hat{n}_a \\right) \\cdot \\left( {\\mathbf p}_i \\times \\hat{n}_a \\right) \\tag{8.9}\n",
+    "I^{S/O}_{a} \\triangleq \\sum_i m_i \\left( {\\mathbf p}_i \\times \\hat{\\bf n}_a \\right) \\cdot \\left( {\\mathbf p}_i \\times \\hat{\\bf n}_a \\right) \\tag{8.9}\n",
     "$$\n",
     "\n",
     "#### Moment of inertia of a continua\n",
     "\n",
     "$$\n",
-    "I^{B/O}_{a} \\triangleq \\int \\mathrm{d}m  \\left( {\\mathbf p}_i \\times \\hat{n}_a \\right) \\cdot \\left( {\\mathbf p}_i \\times \\hat{n}_a \\right) \\tag{8.10}\n",
+    "I^{B/O}_{a} \\triangleq \\int \\mathrm{d}m  \\left( {\\mathbf p}_i \\times \\hat{\\bf n}_a \\right) \\cdot \\left( {\\mathbf p}_i \\times \\hat{\\bf n}_a \\right) \\tag{8.10}\n",
     "$$\n",
     "\n",
     "```{figure} ./images/22.png\n",
@@ -320,8 +320,8 @@
     "```\n",
     "\n",
     "* $P$ is a particle of mass $m$.\n",
-    "* $\\hat{n}_x,\\;\\hat{n}_y,\\;\\hat{n}_z$ are unit vectors that are mutually orthogonal.\n",
-    "* $\\vec{r} = x\\hat{n}_x + y\\hat{n}_y + z\\hat{n}_z$\n",
+    "* $\\hat{\\bf n}_x,\\;\\hat{\\bf n}_y,\\;\\hat{\\bf n}_z$ are unit vectors that are mutually orthogonal.\n",
+    "* ${\\bf r} = x\\hat{\\bf n}_x + y\\hat{\\bf n}_y + z\\hat{\\bf n}_z$\n",
     "\n",
     "**Find**:\n",
     "\n",
@@ -354,7 +354,7 @@
    "source": [
     "- From the previous example, we now have some insight that we will be interested in computing the moments of inertia and products of inertia about a set of unit vectors that make up a reference frame.\n",
     "\n",
-    "- For this discussion, we assume that the unit vectors are: $\\hat{n}_x,\\;\\hat{n}_y,\\;\\hat{n}_z$.\n",
+    "- For this discussion, we assume that the unit vectors are: $\\hat{\\bf n}_x,\\;\\hat{\\bf n}_y,\\;\\hat{\\bf n}_z$.\n",
     "\n",
     "- The inertia scalars can be used to define a square matrix called the inertia matrix.\n",
     "\n",