Add list of objects (e.g., points) extension to standard notation (Ro…

…botLocomotion#11932).

multibody/multibody_doxygen.h

@@ -281,17 +281,19 @@ case, the assumed expressed-in frame is frame F's basis. Alternately, to use a
 different expressed-in frame, say W, typeset with the bracket notation:
 @f$[^Fv^P]_W@f$.
 
+Kane/monogram notation was developed decades ago for kinematics and dynamics.
+It explicitly communicates the quantity being measured and how it is expressed.
 The typeset symbol @f$^Fv^P@f$ is translated to monogram notation as `v_FP`.
 The quantity type always comes first, then an underscore, then left and right
-superscripts.  The symbol `v_FP` implies the vector is expressed in frame F.
-Alternately, to express in frame W, we typeset as @f$[^Fv^P]_W@f$ and use the
-monogram notation `v_FP_W` (adding a final underscore and expressed-in frame W).
+superscripts.  By default, the symbol `v_FP` implies the vector is expressed in
+frame F. Alternately, to express in frame W, use the typeset @f$[^Fv^P]_W@f$ and
+monogram notation `v_FP_W` (add a final underscore and expressed-in frame W).
 We adhere to this pattern for all quantities and it is quite useful once you get
 familiar with it. As a second example, consider the position vector of point Bcm
 (body B's center of mass) from point Bo (the origin of frame B), expressed in B.
-In full typeset, this is @f$[^{B_o}p^{B_{cm}}]_B @f$ whereas in implicit typeset
-this can be abbreviated @f$^Bp^{B_{cm}}@f$ (where the left-superscript B denotes
-Bo and the expressed-in frame is implied to be B). The corresponding
+In explicit typeset, this is @f$[^{B_o}p^{B_{cm}}]_B @f$ whereas in implicit
+typeset this is abbreviated @f$^Bp^{B_{cm}}@f$ (where the left-superscript B
+denotes Bo and the expressed-in frame is implied to be B). The corresponding
 monogram equivalents are `p_BoBcm_B` and `p_BBcm`, respectively.
 
 Here are some more useful multibody quantities.
@@ -301,7 +303,7 @@ source file. However, each row must be specified on a single line of text. You
 can violate the 80-character style guide limit if you have to, but be
 reasonable! Alternately, use a footnote to avoid running over. -->
 
-Quantity             |Symbol|     Typeset              |   Code     | Meaning †
+Quantity             |Symbol|     Typeset              | Monogram   | Meaning †
 ---------------------|:----:|:------------------------:|:----------:|----------------------------
 Rotation matrix      |  R   |@f$^BR^C@f$               |`R_BC`      |Frame C's orientation in frame B
 Position vector      |  p   |@f$^Pp^Q@f$               |`p_PQ`      |Position from point P to point Q
@@ -319,6 +321,7 @@ Inertia matrix       |  I   |@f$I^{B/Bo}@f$            |`I_BBo`     |Body B's in
 Spatial inertia      |  M   |@f$M^{B/Bo}@f$            |`M_BBo`     |Body B's spatial inertia about Bo †
 Jacobian wrt q †††   | Jq   |@f$[J_{q}^{{}^Pp^Q}]_E@f$ |`Jq_p_PQ_E` |Q's position Jacobian from P <b>in</b> E wrt q
 Jacobian wrt q̇       | Jqdot|@f$J_{q̇}^{{}^Bv^Q}@f$     |`Jqdot_v_BQ`|Q's translational velocity Jacobian in B wrt q̇
+Jacobian wrt v       | Jv   |@f$J_{v}^{{}^Bv^Q}@f$     |`Jv_v_BQ`   |Q's translational velocity Jacobian in B wrt v
 Jacobian wrt v       | Jv   |@f$J_{v}^{{}^B\omega^C}@f$|`Jv_w_BC`   |C's angular velocity Jacobian in B wrt v
 
 † In code, a vector has an expressed-in-frame which appears after the quantity.
@@ -356,7 +359,19 @@ B and when there are no motion constraints (no relationships between q̇₁ ...
 @f$\;[J_{q}^{{}^{Bo}p^Q}]_B = [J_{q̇}^{{}^Bv^Q}]_B\;@f$ i.e.,
 `(Jq_p_BoQ_B = Jqdot_v_BQ_B)`.
 
-Next topic: @ref Dt_multibody_quantities
+Monogram notation addresses frequently used kinematics.  In a context-sensible
+way (and in collaboration with reviewers), extend notation to related concepts.
+Some examples are shown below.
+Extended notation         || Description (herein E is the vectors' expressed-in-frame)
+:------------------------:||---------------------------------------------
+p_PQset_E  | p_PQlist_E   |  Set of position vectors from a point P to each of the points in the set Q = {Q₀, Q₁, Q₂, ...}
+v_BQset_E  | v_BQlist_E   |  Set of translational velocities in frame B for the set of points Q = {Q₀, Q₁, Q₂, ...}
+w_BCset_E  | w_BClist_E   |  Set of angular velocities in frame B for the frames in the set C = {C₀, C₁, C₂, ...}
+vset_E     | vlist_E      |  Set of generic vectors v = {v₀,  v₁,  v₂} expressed in frame E
+mesh_B                    || A mesh whose underlying vertices' positions are from Bo (frame B's origin), expressed in frame B
+point_cloud_B             || A point cloud whose underlying points' positions are from Bo (frame B's origin), expressed in frame B
+
+ Next topic: @ref Dt_multibody_quantities
 */
 
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