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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/notation.rst b/notation.rst index 385e9a2d..95b67877 100644 --- a/notation.rst +++ b/notation.rst @@ -323,3 +323,35 @@ Lagrange's method in $\ddot{\bar{q}}$ in the inertial forces and the generalized conservative forces considered in the Lagrangian. +Figure Sign Conventions +======================= + +:numref:`fig-sign-convention-translation` shows three ways to indicate leader +arrows on the dimension for the distance between points :math:`P` and :math:`Q` +parallel to :math:`\hat{n}_x`. A positive value of :math:`q` indicates that +point :math:`Q` is to the right of point :math:`P` and that +:math:`\bar{r}^{Q/P} \cdot \hat{n}_x = q` and :math:`\bar{r}^{P/Q} \cdot +\hat{n}_x = -q`. + +.. _fig-sign-convention-translation: +.. figure:: figures/sign-convention-translation.svg + + Three options for adding arrows to linear dimensions which all have the same + meaning. + +In the first row (a, b, c) of :numref:`fig-sign-convention-orientation` there +are three ways to indicate leader arrows on the angular dimension :math:`q` for +a positive right handed orientation of :math:`A` with respect to :math:`N`. A +positive value of :math:`q` gives a positive right handed orientation. This +corresponds to the SymPy Mechanics command ``A.orient_axis(N, q, N.z)``. In the +second row (d, e, f), three ways are shown to indicate leader arrows on the +angular dimension :math:`q` for a negative right handed orientation of +:math:`A` with respect to :math:`N`. A positive value of :math:`q` causes a +negative right handed orientation. This row corresponds to the SymPy Mechanics +commands ``A.orient_axis(N, -q, N.z)`` or ``A.orient_axis(N, q, -N.z)``. + +.. _fig-sign-convention-orientation: +.. figure:: figures/sign-convention-orientation.svg + + Options for adding arrows to angular dimensions for positive (first row) and + negative (second row) orientations. From 831d85df762db20a21fd4cfebc07e38024be84b6 Mon Sep 17 00:00:00 2001 From: "Jason K. Moore" Date: Wed, 20 Mar 2024 10:03:30 +0100 Subject: [PATCH 02/10] Added double arrows to snakeboard dimensions. --- figures/motion-snakeboard.svg | 31787 ++++++++++++++------------------ 1 file changed, 13774 insertions(+), 18013 deletions(-) diff --git a/figures/motion-snakeboard.svg b/figures/motion-snakeboard.svg index 0a1bfc4e..fd4b8d4c 100644 --- a/figures/motion-snakeboard.svg +++ b/figures/motion-snakeboard.svg @@ -1,18024 +1,13785 @@ + + - - - - image/svg+xml - - - - - + inkscape:version="1.2.2 (b0a8486541, 2022-12-01)" + xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape" + xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd" + xmlns="http://www.w3.org/2000/svg" + xmlns:svg="http://www.w3.org/2000/svg"> + id="defs6" /> + inkscape:zoom="0.29734126" + inkscape:cx="437.20807" + inkscape:cy="299.31937" + inkscape:window-width="2560" + inkscape:window-height="1403" + inkscape:window-x="2560" + inkscape:window-y="0" + inkscape:window-maximized="1" + inkscape:current-layer="g10"> + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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Moore" Date: Wed, 20 Mar 2024 10:29:56 +0100 Subject: [PATCH 04/10] Added negative sign to orientation. --- figures/sign-convention-orientation.svg | 49367 ++++++++++++---------- 1 file changed, 26648 insertions(+), 22719 deletions(-) diff --git a/figures/sign-convention-orientation.svg b/figures/sign-convention-orientation.svg index e69dac0f..213844ec 100644 --- a/figures/sign-convention-orientation.svg +++ b/figures/sign-convention-orientation.svg @@ -2,19 +2,21 @@ + - + inkscape:current-layer="g36828"> + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/notation.rst b/notation.rst index 95b67877..e775a693 100644 --- a/notation.rst +++ b/notation.rst @@ -326,6 +326,7 @@ Lagrange's method Figure Sign Conventions ======================= + :numref:`fig-sign-convention-translation` shows three ways to indicate leader arrows on the dimension for the distance between points :math:`P` and :math:`Q` parallel to :math:`\hat{n}_x`. A positive value of :math:`q` indicates that @@ -355,3 +356,7 @@ commands ``A.orient_axis(N, -q, N.z)`` or ``A.orient_axis(N, q, -N.z)``. Options for adding arrows to angular dimensions for positive (first row) and negative (second row) orientations. + + +.. _fig-vector-sign-convention: +.. figure:: figures/notation-vector-sign-convention.svg From 37ea2753dbab5f8660e0b5d7303287d291697c93 Mon Sep 17 00:00:00 2001 From: "Jason K. Moore" Date: Wed, 20 Mar 2024 10:54:02 +0100 Subject: [PATCH 06/10] Final draft of the sign convention explanation. --- ...tion-linear-dimension-sign-convention.svg} | 0 ...on-rotation-dimension-sign-convention.svg} | 0 notation.rst | 62 ++++++++++++------- 3 files changed, 39 insertions(+), 23 deletions(-) rename figures/{sign-convention-translation.svg => notation-linear-dimension-sign-convention.svg} (100%) rename figures/{sign-convention-orientation.svg => notation-rotation-dimension-sign-convention.svg} (100%) diff --git a/figures/sign-convention-translation.svg b/figures/notation-linear-dimension-sign-convention.svg similarity index 100% rename from figures/sign-convention-translation.svg rename to figures/notation-linear-dimension-sign-convention.svg diff --git a/figures/sign-convention-orientation.svg b/figures/notation-rotation-dimension-sign-convention.svg similarity index 100% rename from figures/sign-convention-orientation.svg rename to figures/notation-rotation-dimension-sign-convention.svg diff --git a/notation.rst b/notation.rst index e775a693..56d9ee8f 100644 --- a/notation.rst +++ b/notation.rst @@ -326,37 +326,53 @@ Lagrange's method Figure Sign Conventions ======================= - -:numref:`fig-sign-convention-translation` shows three ways to indicate leader -arrows on the dimension for the distance between points :math:`P` and :math:`Q` -parallel to :math:`\hat{n}_x`. A positive value of :math:`q` indicates that -point :math:`Q` is to the right of point :math:`P` and that -:math:`\bar{r}^{Q/P} \cdot \hat{n}_x = q` and :math:`\bar{r}^{P/Q} \cdot +:numref:`fig-notation-linear-dimension-sign-convention` shows three ways to +indicate leader arrows on the dimension for the distance between points +:math:`P` and :math:`Q` parallel to :math:`\hat{n}_x`. A positive value of +:math:`q` indicates that point :math:`Q` is to the right of point :math:`P` and +that :math:`\bar{r}^{Q/P} \cdot \hat{n}_x = q` and :math:`\bar{r}^{P/Q} \cdot \hat{n}_x = -q`. -.. _fig-sign-convention-translation: -.. figure:: figures/sign-convention-translation.svg +.. _fig-notation-linear-dimension-sign-convention: +.. figure:: figures/notation-linear-dimension-sign-convention.svg Three options for adding arrows to linear dimensions which all have the same meaning. -In the first row (a, b, c) of :numref:`fig-sign-convention-orientation` there -are three ways to indicate leader arrows on the angular dimension :math:`q` for -a positive right handed orientation of :math:`A` with respect to :math:`N`. A -positive value of :math:`q` gives a positive right handed orientation. This -corresponds to the SymPy Mechanics command ``A.orient_axis(N, q, N.z)``. In the -second row (d, e, f), three ways are shown to indicate leader arrows on the -angular dimension :math:`q` for a negative right handed orientation of -:math:`A` with respect to :math:`N`. A positive value of :math:`q` causes a -negative right handed orientation. This row corresponds to the SymPy Mechanics -commands ``A.orient_axis(N, -q, N.z)`` or ``A.orient_axis(N, q, -N.z)``. - -.. _fig-sign-convention-orientation: -.. figure:: figures/sign-convention-orientation.svg +In the first row (a, b, c) of :numref:`fig-notation-rotation-sign-convention` +there are three ways to indicate leader arrows on the angular dimension +:math:`q` for a positive right handed orientation of :math:`A` with respect to +:math:`N`. A positive value of :math:`q` gives a positive right handed +orientation. This corresponds to the SymPy Mechanics command ``A.orient_axis(N, +q, N.z)``. In the second row (d, e, f), three ways are shown to indicate leader +arrows on the angular dimension :math:`q` for a negative right handed +orientation of :math:`A` with respect to :math:`N`. A positive value of +:math:`q` causes a negative right handed orientation. This row corresponds to +the SymPy Mechanics commands ``A.orient_axis(N, -q, N.z)`` or +``A.orient_axis(N, q, -N.z)``. In g) a negative sign is indicated on :math:`q`. +It is sometimes convenient to draw the rotation in negative right handed +rotation and by labeling the value :math:`-q` g) is equivalent to a). We try to +do this sparingly. + +.. _fig-notation-rotation-dimension-sign-convention: +.. figure:: figures/notation-rotation-dimension-sign-convention.svg Options for adding arrows to angular dimensions for positive (first row) and negative (second row) orientations. - -.. _fig-vector-sign-convention: +In figure :numref:`fig-notation-vector-sign-convention` various vectors are shown. +Vectors are always drawn with a single arrow to indicate the positive sense of +the vector. In a) the vector acting on body :math:`A` is :math:`-F\hat{n}_x` +and the vector actin gon body :math:`B` is :math:`F\hax{n}_x`. The variable +:math:`F` indicated beside the arrow means that a positive value of :math:`F` +has the corresponding sense as the vector arrow head. The sense changes for +both vectors in b) and for one in c). In d), a negative :math:`F` is indicated. +This makes d) equivalent to a). The negative sense for that vector is shown +when :math:`-F` is beside it. + +.. _fig-notation-vector-sign-convention: .. figure:: figures/notation-vector-sign-convention.svg + + Various ways to draw vector arrows, where the arrow head indicates the + positive sense of the vector if the variable is positive and negative sense + if the variable is shown as negative. From 86f69e1300537b98dda667e84131c81aaca836a9 Mon Sep 17 00:00:00 2001 From: "Jason K. Moore" Date: Wed, 20 Mar 2024 11:34:54 +0100 Subject: [PATCH 07/10] Some improvements to the wording on the sign convention section. --- notation.rst | 38 +++++++++++++++++++------------------- 1 file changed, 19 insertions(+), 19 deletions(-) diff --git a/notation.rst b/notation.rst index 56d9ee8f..ef498f9c 100644 --- a/notation.rst +++ b/notation.rst @@ -343,16 +343,16 @@ In the first row (a, b, c) of :numref:`fig-notation-rotation-sign-convention` there are three ways to indicate leader arrows on the angular dimension :math:`q` for a positive right handed orientation of :math:`A` with respect to :math:`N`. A positive value of :math:`q` gives a positive right handed -orientation. This corresponds to the SymPy Mechanics command ``A.orient_axis(N, -q, N.z)``. In the second row (d, e, f), three ways are shown to indicate leader -arrows on the angular dimension :math:`q` for a negative right handed -orientation of :math:`A` with respect to :math:`N`. A positive value of -:math:`q` causes a negative right handed orientation. This row corresponds to -the SymPy Mechanics commands ``A.orient_axis(N, -q, N.z)`` or +orientation in a), b), and c). This corresponds to the SymPy Mechanics command +``A.orient_axis(N, q, N.z)``. In the second row (d, e, f), three ways are shown +to indicate leader arrows on the angular dimension :math:`q` for a negative +right handed orientation of :math:`A` with respect to :math:`N`. A positive +value of :math:`q` causes a negative right handed orientation. This row +corresponds to the SymPy Mechanics commands ``A.orient_axis(N, -q, N.z)`` or ``A.orient_axis(N, q, -N.z)``. In g) a negative sign is indicated on :math:`q`. It is sometimes convenient to draw the rotation in negative right handed -rotation and by labeling the value :math:`-q` g) is equivalent to a). We try to -do this sparingly. +rotation and by labeling the value :math:`-q`. This means that g) is equivalent +to a). We try to do this sparingly. .. _fig-notation-rotation-dimension-sign-convention: .. figure:: figures/notation-rotation-dimension-sign-convention.svg @@ -360,19 +360,19 @@ do this sparingly. Options for adding arrows to angular dimensions for positive (first row) and negative (second row) orientations. -In figure :numref:`fig-notation-vector-sign-convention` various vectors are shown. -Vectors are always drawn with a single arrow to indicate the positive sense of -the vector. In a) the vector acting on body :math:`A` is :math:`-F\hat{n}_x` -and the vector actin gon body :math:`B` is :math:`F\hax{n}_x`. The variable -:math:`F` indicated beside the arrow means that a positive value of :math:`F` -has the corresponding sense as the vector arrow head. The sense changes for -both vectors in b) and for one in c). In d), a negative :math:`F` is indicated. -This makes d) equivalent to a). The negative sense for that vector is shown -when :math:`-F` is beside it. +In figure :numref:`fig-notation-vector-sign-convention` various vectors are +shown. Vectors are always drawn with a single arrow to indicate the positive +sense of the vector. In a) the vector acting on body :math:`A` is +:math:`-F\hat{n}_x` and the vector acting on body :math:`B` is +:math:`F\hax{n}_x`. The variable :math:`F` indicated beside the arrow means +that a positive value of :math:`F` has the corresponding sense as the vector +arrow head. The sense changes for both vectors in b) and for one vector in c). +In d), a negative :math:`F` is indicated. This makes d) equivalent to a). The +negative sense for that vector is shown when :math:`-F` is beside it. .. _fig-notation-vector-sign-convention: .. figure:: figures/notation-vector-sign-convention.svg Various ways to draw vector arrows, where the arrow head indicates the - positive sense of the vector if the variable is positive and negative sense - if the variable is shown as negative. + positive sense of the vector if the variable has no sign and negative sense + if the variable has a negative sign. From 0c865fb02eb67839ed53042d65310ed89df341a4 Mon Sep 17 00:00:00 2001 From: "Jason K. Moore" Date: Wed, 20 Mar 2024 14:38:34 +0100 Subject: [PATCH 08/10] Fixed the latex error. --- notation.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/notation.rst b/notation.rst index ef498f9c..411c6225 100644 --- a/notation.rst +++ b/notation.rst @@ -364,7 +364,7 @@ In figure :numref:`fig-notation-vector-sign-convention` various vectors are shown. Vectors are always drawn with a single arrow to indicate the positive sense of the vector. In a) the vector acting on body :math:`A` is :math:`-F\hat{n}_x` and the vector acting on body :math:`B` is -:math:`F\hax{n}_x`. The variable :math:`F` indicated beside the arrow means +:math:`F\hat{n}_x`. The variable :math:`F` indicated beside the arrow means that a positive value of :math:`F` has the corresponding sense as the vector arrow head. The sense changes for both vectors in b) and for one vector in c). In d), a negative :math:`F` is indicated. This makes d) equivalent to a). The From a7e98eadad1f1a7be5563af9ad95283f4d1fe3fe Mon Sep 17 00:00:00 2001 From: "Jason K. Moore" Date: Wed, 20 Mar 2024 15:32:49 +0100 Subject: [PATCH 09/10] Reordered and added a few more notes based on Karien and Peter's comments. --- notation.rst | 61 +++++++++++++++++++++++++++++++--------------------- 1 file changed, 37 insertions(+), 24 deletions(-) diff --git a/notation.rst b/notation.rst index 411c6225..41122021 100644 --- a/notation.rst +++ b/notation.rst @@ -326,6 +326,41 @@ Lagrange's method Figure Sign Conventions ======================= +Vectors +------- + +.. _fig-notation-rotation-dimension-sign-convention: +.. figure:: figures/notation-rotation-dimension-sign-convention.svg + + Options for adding arrows to angular dimensions for positive (first row) and + negative (second row) orientations. + +In figure :numref:`fig-notation-vector-sign-convention` various vectors are +shown. Vectors are always drawn with a single arrow to indicate the positive +sense of the vector. In a) the vector acting on body :math:`A` is +:math:`-F\hat{n}_x` and the vector acting on body :math:`B` is +:math:`F\hat{n}_x`. The variable :math:`F` indicated beside the arrow means +that a positive value of :math:`F` has the corresponding sense as the vector +arrow head. The sense changes for both vectors in b) and for one vector in c). +In d), a negative :math:`F` is indicated. This makes d) equivalent to a). The +negative sense for that vector is shown when :math:`-F` is beside it. + +.. _fig-notation-vector-sign-convention: +.. figure:: figures/notation-vector-sign-convention.svg + + Various ways to draw vector arrows, where the arrow head indicates the + positive sense of the vector if the variable has no sign and negative sense + if the variable has a negative sign. + +Dimensions +---------- + +When we draw dimensions (linear or angular) the arrow heads (or absence of +arrow heads) do not indicate anything about the "sense" of the dimension. A +dimension can take on positive and negative values and you have to rely on the +sense of reference frame unit vectors to know what configuration occurs if a +positive or negative value is given for a dimension. + :numref:`fig-notation-linear-dimension-sign-convention` shows three ways to indicate leader arrows on the dimension for the distance between points :math:`P` and :math:`Q` parallel to :math:`\hat{n}_x`. A positive value of @@ -337,7 +372,8 @@ that :math:`\bar{r}^{Q/P} \cdot \hat{n}_x = q` and :math:`\bar{r}^{P/Q} \cdot .. figure:: figures/notation-linear-dimension-sign-convention.svg Three options for adding arrows to linear dimensions which all have the same - meaning. + meaning. Follow the right hand rule to know the positive sense of an + orientation. In the first row (a, b, c) of :numref:`fig-notation-rotation-sign-convention` there are three ways to indicate leader arrows on the angular dimension @@ -353,26 +389,3 @@ corresponds to the SymPy Mechanics commands ``A.orient_axis(N, -q, N.z)`` or It is sometimes convenient to draw the rotation in negative right handed rotation and by labeling the value :math:`-q`. This means that g) is equivalent to a). We try to do this sparingly. - -.. _fig-notation-rotation-dimension-sign-convention: -.. figure:: figures/notation-rotation-dimension-sign-convention.svg - - Options for adding arrows to angular dimensions for positive (first row) and - negative (second row) orientations. - -In figure :numref:`fig-notation-vector-sign-convention` various vectors are -shown. Vectors are always drawn with a single arrow to indicate the positive -sense of the vector. In a) the vector acting on body :math:`A` is -:math:`-F\hat{n}_x` and the vector acting on body :math:`B` is -:math:`F\hat{n}_x`. The variable :math:`F` indicated beside the arrow means -that a positive value of :math:`F` has the corresponding sense as the vector -arrow head. The sense changes for both vectors in b) and for one vector in c). -In d), a negative :math:`F` is indicated. This makes d) equivalent to a). The -negative sense for that vector is shown when :math:`-F` is beside it. - -.. _fig-notation-vector-sign-convention: -.. figure:: figures/notation-vector-sign-convention.svg - - Various ways to draw vector arrows, where the arrow head indicates the - positive sense of the vector if the variable has no sign and negative sense - if the variable has a negative sign. From 6779d4585804dacb957d1baafcc6d849dcc80baa Mon Sep 17 00:00:00 2001 From: "Jason K. Moore" Date: Wed, 20 Mar 2024 15:38:06 +0100 Subject: [PATCH 10/10] Fixed figure order. --- notation.rst | 39 ++++++++++++++++++++------------------- 1 file changed, 20 insertions(+), 19 deletions(-) diff --git a/notation.rst b/notation.rst index 41122021..f66e55e1 100644 --- a/notation.rst +++ b/notation.rst @@ -329,12 +329,6 @@ Figure Sign Conventions Vectors ------- -.. _fig-notation-rotation-dimension-sign-convention: -.. figure:: figures/notation-rotation-dimension-sign-convention.svg - - Options for adding arrows to angular dimensions for positive (first row) and - negative (second row) orientations. - In figure :numref:`fig-notation-vector-sign-convention` various vectors are shown. Vectors are always drawn with a single arrow to indicate the positive sense of the vector. In a) the vector acting on body :math:`A` is @@ -375,17 +369,24 @@ that :math:`\bar{r}^{Q/P} \cdot \hat{n}_x = q` and :math:`\bar{r}^{P/Q} \cdot meaning. Follow the right hand rule to know the positive sense of an orientation. -In the first row (a, b, c) of :numref:`fig-notation-rotation-sign-convention` -there are three ways to indicate leader arrows on the angular dimension -:math:`q` for a positive right handed orientation of :math:`A` with respect to -:math:`N`. A positive value of :math:`q` gives a positive right handed -orientation in a), b), and c). This corresponds to the SymPy Mechanics command -``A.orient_axis(N, q, N.z)``. In the second row (d, e, f), three ways are shown -to indicate leader arrows on the angular dimension :math:`q` for a negative +In the first row (a, b, c) of +:numref:`fig-notation-rotation-dimension-sign-convention` there are three ways +to indicate leader arrows on the angular dimension :math:`q` for a positive right handed orientation of :math:`A` with respect to :math:`N`. A positive -value of :math:`q` causes a negative right handed orientation. This row -corresponds to the SymPy Mechanics commands ``A.orient_axis(N, -q, N.z)`` or -``A.orient_axis(N, q, -N.z)``. In g) a negative sign is indicated on :math:`q`. -It is sometimes convenient to draw the rotation in negative right handed -rotation and by labeling the value :math:`-q`. This means that g) is equivalent -to a). We try to do this sparingly. +value of :math:`q` gives a positive right handed orientation in a), b), and c). +This corresponds to the SymPy Mechanics command ``A.orient_axis(N, q, N.z)``. +In the second row (d, e, f), three ways are shown to indicate leader arrows on +the angular dimension :math:`q` for a negative right handed orientation of +:math:`A` with respect to :math:`N`. A positive value of :math:`q` causes a +negative right handed orientation. This row corresponds to the SymPy Mechanics +commands ``A.orient_axis(N, -q, N.z)`` or ``A.orient_axis(N, q, -N.z)``. In g) +a negative sign is indicated on :math:`q`. It is sometimes convenient to draw +the rotation in negative right handed rotation and by labeling the value +:math:`-q`. This means that g) is equivalent to a). We try to do this +sparingly. + +.. _fig-notation-rotation-dimension-sign-convention: +.. figure:: figures/notation-rotation-dimension-sign-convention.svg + + Options for adding arrows to angular dimensions for positive (first row) and + negative (second row) orientations.