diff --git a/docs/lecture02.ipynb b/docs/lecture02.ipynb
index 4da8c93..9dc9ee3 100644
--- a/docs/lecture02.ipynb
+++ b/docs/lecture02.ipynb
@@ -50,27 +50,34 @@
    },
    "source": [
     "Particle kinematics is the application of special relativity to elementary particle reactions.\n",
+    "In experiments, the \"beam\" collides onto the \"target\" with high energy to create other particles.\n",
+    "\n",
+    "Each particle has a 4-vector $p^{\\mu}$:\n",
+    "\n",
+    "$$\n",
+    "p^{\\mu} = (E, p_x, p_y, p_z) = (E, \\vec{p}) \n",
+    "$$\n",
     "\n",
     "Two frames that are commonly used are the Center of Mass (CoM) frame and the laboratory (Lab) frame.\n",
     "\n",
-    "For a two-particle reaction,\n",
-    "$a+b \\to 1 + ... + n$, the frames satisfy the following relations."
+    "For a two-particle reaction, $a+b \\to 1 + ... + n$, the frames satisfy the following relations. \n",
+    "- **Lab frame**: $\\vec{p}_b = \\vec{0}$<br>\n",
+    "  Target particle $b$ is at rest, while beam particle $a$ is moving.\n",
+    "- **CoM frame**: $\\vec{p}_a+\\vec{p}_b = \\vec{0}$<br>\n",
+    "  The total momentum is zero, i.e., the momenta of the two initial state particles have opposite direction."
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "source": [
-    "- **Lab frame**: $\\vec{p}_b = \\vec{0}$<br>\n",
-    "  Target particle $b$ is at rest, while beam particle $a$ is moving.\n",
-    "- **CoM frame**: $\\vec{p}_a+\\vec{p}_b = \\vec{0}$<br>\n",
-    "  The total momentum is zero, i.e., the momenta of the two initial state particles have opposite direction."
+    "Masses can be defined as a Lorentz invariant quantity (unaffected by reference frame):\n",
+    "\n",
+    "$$\n",
+    " p^2_i = E^2_i = |\\vec{p}_i|^2 = m^2_i\n",
+    "$$\n",
+    "\n",
+    "where $p$ is the 4-vector, $E$ is the energy, $\\vec{p}$ is the three vector, and $m$ is the mass."
    ]
   },
   {
@@ -96,7 +103,7 @@
     "tags": []
    },
    "source": [
-    "We now see a simple situation of two-body decay ($n=2$), i.e., $a+b \\rightarrow 1+2$"
+    "Let us now consider the case of a two-body decay ($n=2$), i.e., $a+b \\rightarrow 1+2$."
    ]
   },
   {
@@ -109,7 +116,10 @@
     "tags": []
    },
    "source": [
-    "```{image} https://github.com/ComPWA/tensorwaves/assets/17490173/9d5e1cf4-43a9-4670-873a-0833ae024cba\n",
+    "```{image} https://github.com/ComPWA/strong2020-salamanca/assets/29308176/d1cac039-0c13-4d28-b537-4ba2f66064b6\n",
+    ":width: 300px\n",
+    "```\n",
+    "```{image} https://github.com/ComPWA/strong2020-salamanca/assets/29308176/7665969c-31a9-4b65-9ce9-318e2ca6fdb3\n",
     ":width: 300px\n",
     "```"
    ]
@@ -124,10 +134,9 @@
     "tags": []
    },
    "source": [
-    "<!-- In the case of the scattering happens in the x-z plane for both frames, the two frames are related by a boost along the z axis. -->\n",
-    "When we have a final state with two particles ($n=2$), we can define one $x-z$ plane that is spanned by the momenta of the two final state particles in the Lab frame. The CoM frame and the Lab frame can now be related by a boost along the $z$-axis (the direction of particle $a$).\n",
+    "When we have a final state with two particles ($n=2$), we can define one $xz$ plane that is spanned by the momenta of the two final state particles in the Lab frame. The CoM frame and the Lab frame can now be related by a boost along the $z$-axis (the direction of particle $a$).\n",
     "\n",
-    "With this definition of the x-z plane, we have:\n",
+    "With this definition of the $xz$ plane, we have:\n",
     "- $\\vec{z}$ is parallel to the beam $\\vec{p}_a$\n",
     "- $\\vec{y} $ is parallel to $ \\vec{p}_a \\times \\vec{p}_1$"
    ]
@@ -155,7 +164,7 @@
     "tags": []
    },
    "source": [
-    "The Lorentz transformation, which includes both boosts (velocity changes) and rotations, is crucial for understanding how the properties of particles, such as position and time, transform between different inertial frames in relative motion."
+    "Lorentz transformations, can be factorized into rotations and boosts along one axis (or arbitrary direction) and are required for transforming particle properties, such as position and time, between different inertial frames in relative motion."
    ]
   },
   {
@@ -168,7 +177,7 @@
     "tags": []
    },
    "source": [
-    "### Boost (between Lab and CoM)"
+    "### Boost along one axis"
    ]
   },
   {
@@ -181,7 +190,7 @@
     "tags": []
    },
    "source": [
-    "Only the energy and the $z$ component of the four-momenta changes, so we can write the Lorentz boost with a 2D matrix."
+    "When we boost in the direction of the $z$ axis, only the energy and the $z$ component of the four-momenta changes, so we can express the Lorentz boost as a 2D matrix:"
    ]
   },
   {
@@ -206,7 +215,7 @@
     "\\begin{pmatrix}\n",
     " E^L\\\\\n",
     " p^L_z\n",
-    "\\end{pmatrix}\n",
+    "\\end{pmatrix},\n",
     "$$"
    ]
   },
@@ -214,7 +223,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Given the inverse relation"
+    "and its inverse relation,"
    ]
   },
   {
@@ -233,8 +242,8 @@
     "\\begin{pmatrix}\n",
     " E^*\\\\\n",
     " p^*_z\n",
-    "\\end{pmatrix}\n",
-    "$$\n",
+    "\\end{pmatrix},\n",
+    "$$ (inverse_relation)\n",
     "\n"
    ]
   },
@@ -242,7 +251,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "With "
+    "with "
    ]
   },
   {
@@ -251,7 +260,7 @@
    "source": [
     "$$\n",
     "\\beta = \\frac{p^*_b}{m_b}\n",
-    "$$"
+    "$$ (beta_label)"
    ]
   },
   {
@@ -273,20 +282,7 @@
    "source": [
     "$$\n",
     "\\gamma \\beta = \\frac{E^*_b}{m_b}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "We check that it brings the target at rest in Exercise below"
+    "$$ (gammabeta_label)"
    ]
   },
   {
@@ -336,7 +332,7 @@
     "\\end{pmatrix}\n",
     "$$\n",
     "\n",
-    "using the relations (3) and (4) and subsititute into (2):\n",
+    "using the relations {eq}`beta_label` and {eq}`gammabeta_label` and subsititute into {eq}`inverse_relation`:\n",
     "\n",
     "\n",
     "$$\\begin{pmatrix}\n",
@@ -372,7 +368,7 @@
     "\\end{pmatrix}\n",
     "$$\n",
     "\n",
-    "When assuming $p_{b,z}^L=0$, then $E_{b}^L = m_b$, and thus\n",
+    "If $p_{b,z}^L=0$ holds, then $E_{b}^L = m_b$, and thus\n",
     "\n",
     "$$p^L_{b,z} = 0$$\n",
     ":::"
@@ -401,28 +397,21 @@
     "tags": []
    },
    "source": [
-    "### Rotation"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "#### Active Rotation"
+    "### Rotations"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Under an active rotation, the momentum is changed and the axes are fixed"
+    "We use active rotations instead of passive rotations. Under an active rotation, the momentum is changed and the axes are fixed"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Example: a momentum of unit length forming an angle θ with the z axis"
+    "Example: if we rotate a momentum of unit length over the $z$ axis with an angle $\\theta$, we get:"
    ]
   },
   {
@@ -438,12 +427,12 @@
     " p_z\n",
     "\\end{pmatrix} =\n",
     "\\begin{pmatrix}\n",
-    " sin(\\theta)\n",
+    " \\sin(\\theta)\n",
     " \\\\\n",
     " 0\n",
     " \\\\\n",
-    " cos(\\theta)\n",
-    "\\end{pmatrix}\n",
+    " \\cos(\\theta)\n",
+    "\\end{pmatrix}.\n",
     "$$ (rotation_label)"
    ]
   },
@@ -451,7 +440,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "After a rotation of ω around y, it forms an angle θ + ω with the z axis"
+    "After a rotation of $\\omega$ around the $y$ axis, the rotated momentum forms an angle $\\theta + \\omega$ with the $z$ axis, we get:"
    ]
   },
   {
@@ -479,22 +468,15 @@
     "\\end{pmatrix}\n",
     "=\n",
     "\\begin{pmatrix}\n",
-    " sin(\\theta+\\omega)\n",
+    " \\sin(\\theta+\\omega)\n",
     " \\\\\n",
     " 0\n",
     " \\\\\n",
-    " cos(\\theta+\\omega)\n",
-    "\\end{pmatrix}\n",
+    " \\cos(\\theta+\\omega)\n",
+    "\\end{pmatrix}.\n",
     "$$"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Now we check the result of the rotation above"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {
@@ -524,16 +506,14 @@
     ":::{solution} check-rotation\n",
     ":class: dropdown\n",
     "\n",
-    "Recall the rotation matrix:\n",
+    "Recall the rotation matrices, any rotation can be decomposed into rotations around $z$ and $y$ axes:\n",
     "\n",
     "$$\n",
     "R_z(\\omega)\n",
     "=\n",
     "\\begin{pmatrix}\n",
-    "cos(\\omega) & -sin(\\omega) & 0\n",
-    "\\\\\n",
-    "sin(\\omega) & cos(\\omega) & 0\n",
-    "\\\\\n",
+    "\\cos(\\omega) & -\\sin(\\omega) & 0 \\\\\n",
+    "\\sin(\\omega) & \\cos(\\omega) & 0 \\\\\n",
     "0 & 0 & 1\n",
     "\\end{pmatrix}\n",
     "$$\n",
@@ -542,99 +522,76 @@
     "R_y(\\omega)\n",
     "=\n",
     "\\begin{pmatrix}\n",
-    "cos(\\omega) & 0 & sin(\\omega) \n",
-    "\\\\\n",
-    "0 & 1 & 0\n",
-    "\\\\\n",
-    "-sin(\\omega) &0 & cos(\\omega) \n",
+    "\\cos(\\omega) & 0 & \\sin(\\omega) \\\\\n",
+    "0 & 1 & 0 \\\\\n",
+    "-\\sin(\\omega) &0 & \\cos(\\omega) \n",
     "\\end{pmatrix}\n",
     "$$\n",
     "\n",
-    "Any rotation can be decomposed into rotations around z and y axes above\n",
-    "\n",
+    "The rotation matrix around $x$ axes is also given for completeness:\n",
     "\n",
     "$$\n",
-    "R_y(\\omega)\n",
+    "R_x(\\omega)\n",
     "=\n",
     "\\begin{pmatrix}\n",
-    "1&0&0\n",
-    "\\\\\n",
-    "0 & cos(\\omega) & -sin(\\omega) \n",
-    "\\\\\n",
-    "0 & sin(\\omega) & cos(\\omega) \n",
+    "1&0&0 \\\\\n",
+    "0 & \\cos(\\omega) & -\\sin(\\omega) \\\\\n",
+    "0 & \\sin(\\omega) & \\cos(\\omega) \n",
     "\\end{pmatrix}\n",
     "$$\n",
     "\n",
-    "The rotation matrix around x axes is also given for completeness.\n",
-    "\n",
-    "Thus equation {eq}`rotation_label` becomes:\n",
+    "With this, we can rewrite equation {eq}`rotation_label` as:\n",
     "\n",
     "$$\n",
     "\\begin{pmatrix}\n",
-    " p_x'\n",
-    " \\\\\n",
-    " p_y'\n",
-    " \\\\\n",
+    " p_x' \\\\\n",
+    " p_y' \\\\\n",
     " p_z'\n",
     "\\end{pmatrix}\n",
     "=\n",
     "R_y(\\omega)\n",
     "\\begin{pmatrix}\n",
-    " p_x\n",
-    " \\\\\n",
-    " p_y\n",
-    " \\\\\n",
+    " p_x \\\\\n",
+    " p_y \\\\\n",
     " p_z\n",
     "\\end{pmatrix}\n",
     "=\n",
     "\\begin{pmatrix}\n",
-    "cos(\\omega) & 0 & sin(\\omega) \n",
-    "\\\\\n",
-    "0 & 1 & 0\n",
-    "\\\\\n",
-    "-sin(\\omega) &0 & cos(\\omega) \n",
+    "\\cos(\\omega) & 0 & \\sin(\\omega) \\\\\n",
+    "0 & 1 & 0 \\\\\n",
+    "-\\sin(\\omega) &0 & \\cos(\\omega) \n",
     "\\end{pmatrix}\n",
     "\\begin{pmatrix}\n",
-    " p_x\n",
-    " \\\\\n",
-    " p_y\n",
-    " \\\\\n",
+    " p_x \\\\\n",
+    " p_y \\\\\n",
     " p_z\n",
     "\\end{pmatrix}\n",
     "$$\n",
     "\n",
     "$$\n",
     "\\begin{pmatrix}\n",
-    " p_x'\n",
-    " \\\\\n",
-    " p_y'\n",
-    " \\\\\n",
+    " p_x' \\\\\n",
+    " p_y' \\\\\n",
     " p_z'\n",
     "\\end{pmatrix}\n",
     "=\n",
     "\\begin{pmatrix}\n",
-    "p_x \\cdot cos(\\omega)+ p_z \\cdot sin(\\omega) \n",
-    "\\\\\n",
-    "p_y\n",
-    "\\\\\n",
-    "-p_x \\cdot sin(\\omega) + p_z \\cdot cos(\\omega) \n",
+    "p_x \\cdot \\cos(\\omega)+ p_z \\cdot \\sin(\\omega) \\\\\n",
+    "p_y \\\\\n",
+    "-p_x \\cdot \\sin(\\omega) + p_z \\cdot \\cos(\\omega) \n",
     "\\end{pmatrix}\n",
     "$$\n",
     "\n",
     "since \n",
     "$\\begin{pmatrix}\n",
-    " p_x\n",
-    " \\\\\n",
-    " p_y\n",
-    " \\\\\n",
+    " p_x \\\\\n",
+    " p_y \\\\\n",
     " p_z\n",
     "\\end{pmatrix}$ =\n",
     "$\\begin{pmatrix}\n",
-    " sin(\\theta)\n",
-    " \\\\\n",
-    " 0\n",
-    " \\\\\n",
-    " cos(\\theta)\n",
+    " \\sin(\\theta) \\\\\n",
+    " 0 \\\\\n",
+    " \\cos(\\theta)\n",
     "\\end{pmatrix}\n",
     "$,\n",
     "and using the trigonometric identities,\n",
@@ -642,27 +599,21 @@
     "\n",
     "$$\n",
     "\\begin{pmatrix}\n",
-    " p_x'\n",
-    " \\\\\n",
-    " p_y'\n",
-    " \\\\\n",
+    " p_x' \\\\\n",
+    " p_y' \\\\\n",
     " p_z'\n",
     "\\end{pmatrix} \n",
     "=\n",
     "\\begin{pmatrix}\n",
-    "sin(\\theta) \\cdot cos(\\omega)+ cos(\\theta) \\cdot sin(\\omega) \n",
-    "\\\\\n",
-    "0\n",
-    "\\\\\n",
-    "-sin(\\theta) \\cdot sin(\\omega) + cos(\\theta) \\cdot cos(\\omega) \n",
+    "\\sin(\\theta) \\cdot \\cos(\\omega)+ \\cos(\\theta) \\cdot \\sin(\\omega) \\\\\n",
+    "0 \\\\\n",
+    "-\\sin(\\theta) \\cdot \\sin(\\omega) + \\cos(\\theta) \\cdot \\cos(\\omega) \n",
     "\\end{pmatrix}\n",
     "=\n",
     "\\begin{pmatrix}\n",
-    "sin(\\theta+\\omega)\n",
-    "\\\\\n",
-    "0\n",
-    "\\\\\n",
-    "cos(\\theta+\\omega) \n",
+    "\\sin(\\theta+\\omega) \\\\\n",
+    "0 \\\\\n",
+    "\\cos(\\theta+\\omega) \n",
     "\\end{pmatrix}\n",
     "$$\n",
     ":::"
@@ -678,7 +629,7 @@
     "tags": []
    },
    "source": [
-    "### Example1: Angles and Boost"
+    "### Example with data"
    ]
   },
   {
@@ -691,10 +642,12 @@
     "tags": []
    },
    "source": [
-    "\n",
-    "```{image} https://github.com/ComPWA/tensorwaves/assets/17490173/9d5e1cf4-43a9-4670-873a-0833ae024cba\n",
+    "```{image} https://github.com/ComPWA/strong2020-salamanca/assets/29308176/d1cac039-0c13-4d28-b537-4ba2f66064b6\n",
     ":width: 300px\n",
-    "```\n"
+    "```\n",
+    "```{image} https://github.com/ComPWA/strong2020-salamanca/assets/29308176/7665969c-31a9-4b65-9ce9-318e2ca6fdb3\n",
+    ":width: 300px\n",
+    "```"
    ]
   },
   {