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basics/index.html

@@ -164,15 +164,13 @@ <h2 id="basic-knowledge-for-spacedyn-user">Basic Knowledge for SpaceDyn User</h2
 <p class="admonition-title">Note</p>
 <p>We do NOT use the DH notation in SpaceDyn.</p>
 </div>
-<ul>
-<li>
 <p>Our rule locates the origin of the coordinate systems with more flexibility. Our rule locates the origin of the frame on each joint and orients the primary axes so that the inertia tensor should be simpler, but admits three position and three orientation parameters among two successive coordinate systems.</p>
-</li>
+<ul>
 <li>
-<p>For the representation of attitude or orientation, we use 3 by 3 direction cosine matrices, coded with a symbol <code>A</code>. For example, <code>A0</code> is the direction cosines to represent the attitude of the body 0. For the other bodies, a matrix <code>AA</code> is used. The advantage of direction cosine is (1) singularity free, (2) we can easily defive Roll-Pitch-Yaw angles, Euler angles, or quartanions, and (3) it is easy to find the mathematical relationship with angular velocity. </p>
+<p>For the representation of attitude or orientation, we use 3 by 3 direction cosine matrices. The advantage of direction cosine is (1) singularity free, (2) we can easily defive Roll-Pitch-Yaw angles, Euler angles, or quartanions, and (3) it is easy to find the mathematical relationship with angular velocity. </p>
 </li>
 <li>
-<p>On the other hand, we frequently need Roll-Pitch-Yaw (RPY) replresentation also. For RPY angles, we use the symbol <code>Q</code>. For example, in order to express the twisting angles between two coordinate systems, we consider $<code>\alpha</code>$ (roll) around $<code>x</code>$-axis, $<code>\beta</code>$ (pitch) around $<code>y</code>$-axis, then $<code>\gumma</code>$ (yaw) around $<code>z</code>$-axis. The set of these angles are coded by <code>Qi</code>.</p>
+<p>On the other hand, we frequently need Roll-Pitch-Yaw (RPY) replresentation also. For example, in order to express the twisting angles between two coordinate systems, we consider <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>α</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\alpha=0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.0037em;">α</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span> (roll) around <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">x</span></span></span></span>-axis, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>β</mi></mrow><annotation encoding="application/x-tex">\beta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.05278em;">β</span></span></span></span> (pitch) around <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span>-axis, then <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>γ</mi></mrow><annotation encoding="application/x-tex">\gamma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.05556em;">γ</span></span></span></span> (yaw) around <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>z</mi></mrow><annotation encoding="application/x-tex">z</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span></span></span></span>-axis.</p>
 </li>
 <li>
 <p>Weak points: The SpaceDyn is not good at dealing with kinematic constraints other than joint axes. It is also weak at dealing with the problems in which a contact point is dynamically changing. For those problems, a good user programming is required to model the constraint forces. </p>

index.html

@@ -229,5 +229,5 @@ <h2 id="acknowledgement">Acknowledgement</h2>
 
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matlab/index.html

@@ -124,6 +124,12 @@ <h2 id="technical-note">Technical Note</h2>
 <p>Since MATLAB doesn't allo 0 for array index, we use <code>R0</code> and <code>c0</code> instead of <code>RR[0]</code> and <code>cc[0]</code>, for example. </p>
 </li>
 <li>
+<p>For the representation of attitude or orientation, we use 3 by 3 direction cosine matrices, coded with a symbol <code>A</code>. For example, <code>A0</code> is the direction cosines to represent the attitude of the body 0. For the other bodies, a matrix <code>AA</code> is used. </p>
+</li>
+<li>
+<p>For Roll-Pitch-Yaw (RPY) angles, we use the symbol <code>Q</code>. For example, in order to express the twisting angles between two coordinate systems, we consider $<code>\alpha</code>$ (roll) around $<code>x</code>$-axis, $<code>\beta</code>$ (pitch) around $<code>y</code>$-axis, then $<code>\gumma</code>$ (yaw) around $<code>z</code>$-axis. The set of these angles are coded by <code>Qi</code>.</p>
+</li>
+<li>
 <p>We use both the input variables and the global variables to pass the values to m-file functions. The input variables inside the braces are the variables changing time to time, such as joint angles, positions, orientations, and so on. The global variables are the ones holding constant once the model is given, such as topological description matrices, kinematics and dynamic parameters. </p>
 </li>
 </ul>