Correct and improve rpy_ball_mobilizer documentation, replace E matrix with standard N matrix.

[mitiguy]

This is one in a series of PRs to help address issue #22630. It updates documentation in rpy_ball_mobilizer.cc and replaces an inconsistent "E" matrix notation with the "N" matrix.

This PR is in preparation for implementation of CalcNDotMatrix(), CalcNplusDotMatrix(), MapQDDotToAcceleration() and MapAccelerationToQDDot() in the rpy_ball_mobilizer class as was done in PR #22698 and PR #22950.

FYI: Since mobilizers are Drake internal classes, after the internal mobilizer work is complete, there will be PRs (code and testing) for the public API in MultibodyPlant to address issue #22630.

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This change is 

[mitiguy]

feature review +@sherm1

Reviewable status: LGTM missing from assignee sherm1(platform)

[sherm1]

Nice, thanks! Feature + platform pending a few comments

Reviewed 1 of 1 files at r1, all commit messages.
Reviewable status: 5 unresolved discussions

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multibody/tree/rpy_ball_mobilizer.cc line 141 at r1 (raw file):

  // the mobilizer F frame, expressed in the F frame.
  //
  // ⌈ ṙ̇ ⌉   ⌈          cos(y) / cos(p),           sin(y) / cos(p),  0 ⌉ ⌈ ω0 ⌉

BTW this looks like rdotdot on my screen rather than rdot. Not sure if that's just a display artifact -- please check. Everything else looks like a single dot.

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multibody/tree/rpy_ball_mobilizer.cc line 189 at r1 (raw file):

  // the mobilizer F frame, expressed in the F frame (thus w_FM_F = N⁺(q) * q̇).
  //
  // ⌈ ω0 ⌉   ⌈ cos(y) * cos(p),  -sin(y),  0 ⌉ ⌈ ṙ̇ ⌉

BTW again the rdot here looks like rdotdot(r̈) rather than (ṙ), while the rdot four lines up looks fine. Could be a display artifact but might really be dotdot?

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multibody/tree/rpy_ball_mobilizer.cc line 211 at r1 (raw file):

  // the mobilizer F frame, expressed in the F frame.
  //
  // ⌈ ṙ̇ ⌉   ⌈          cos(y) / cos(p),           sin(y) / cos(p),  0 ⌉ ⌈ ω0 ⌉

BTW dot dot?

Also, this seems to duplicate the comments above. If so, just write once and reference elsewhere.

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multibody/tree/rpy_ball_mobilizer.cc line 259 at r1 (raw file):

  // invert the simpler equation v = N⁺(q) * q̇, whose matrix form is
  //
  // ⌈ ω0 ⌉   ⌈ cos(y) * cos(p),  -sin(y),  0 ⌉ ⌈ ṙ̇ ⌉

BTW dotdot?

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multibody/tree/rpy_ball_mobilizer.cc line 280 at r1 (raw file):

  // the mobilizer F frame, expressed in the F frame (thus w_FM_F = N⁺(q) * q̇).
  //
  // ⌈ ω0 ⌉   ⌈ cos(y) * cos(p),  -sin(y),  0 ⌉ ⌈ ṙ̇ ⌉

BTW dotdot?

[sherm1]

Reviewed 1 of 1 files at r2, all commit messages.
Reviewable status: 1 unresolved discussion, commits need curation (https://drake.mit.edu/reviewable.html#curated-commits) (waiting on @mitiguy)

[mitiguy]

Reviewable status: commits need curation (https://drake.mit.edu/reviewable.html#curated-commits)

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multibody/tree/rpy_ball_mobilizer.cc line 141 at r1 (raw file):

Previously, sherm1 (Michael Sherman) wrote…

BTW this looks like rdotdot on my screen rather than rdot. Not sure if that's just a display artifact -- please check. Everything else looks like a single dot.

Done.

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multibody/tree/rpy_ball_mobilizer.cc line 189 at r1 (raw file):

Previously, sherm1 (Michael Sherman) wrote…

BTW again the rdot here looks like rdotdot(r̈) rather than (ṙ), while the rdot four lines up looks fine. Could be a display artifact but might really be dotdot?

Done.

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multibody/tree/rpy_ball_mobilizer.cc line 211 at r1 (raw file):

Previously, sherm1 (Michael Sherman) wrote…

BTW dot dot?

Also, this seems to duplicate the comments above. If so, just write once and reference elsewhere.

Done.

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multibody/tree/rpy_ball_mobilizer.cc line 259 at r1 (raw file):

Previously, sherm1 (Michael Sherman) wrote…

BTW dotdot?

Done.

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multibody/tree/rpy_ball_mobilizer.cc line 280 at r1 (raw file):

Previously, sherm1 (Michael Sherman) wrote…

BTW dotdot?

Done.

[mitiguy]

+(status: squashing now)

Reviewable status: complete! all discussions resolved, LGTM from assignee sherm1(platform)