diff --git a/doc/api/toolkits/mplot3d/view_angles.rst b/doc/api/toolkits/mplot3d/view_angles.rst
@@ -57,34 +57,33 @@ To keep it this way, set ``mouserotationstyle: azel``.
 This approach works fine for spherical coordinate plots, where the *z* axis is special;
 however, it leads to a kind of 'gimbal lock' when looking down the *z* axis:
 the plot reacts differently to mouse movement, dependent on the particular
-orientation at hand. Also, 'roll' cannot be controlled.
+orientation at hand. Also, the 'roll' axis about the viewing direction cannot
+be controlled.
 
 As an alternative, there are various mouse rotation styles where the mouse
 manipulates a virtual 'trackball'. In its simplest form (``mouserotationstyle: trackball``),
 the trackball rotates around an in-plane axis perpendicular to the mouse motion
-(it is as if there is a plate laying on the trackball; the plate itself is fixed
+(it is as if there is a flat plate laying on a trackball; the plate itself is fixed
 in orientation, but you can drag the plate with the mouse, thus rotating the ball).
-This is more natural to work with than the ``azel`` style; however,
-the plot cannot be easily rotated around the viewing direction - one has to
-move the mouse in circles with a handedness opposite to the desired rotation,
-counterintuitively.
+This is more natural to work with than the ``azel`` style; however, it is
+difficult and unintuitive to control roll with it.
 
 A different variety of trackball rotates along the shortest arc on the virtual
-sphere (``mouserotationstyle: sphere``). Rotating around the viewing direction
-is straightforward with it: grab the ball near its edge instead of near the center.
+sphere (``mouserotationstyle: sphere``). Rotating roll is straightforward with it:
+grab the ball near its edge instead of near the center.
 
 Ken Shoemake's ARCBALL [Shoemake1992]_ is also available (``mouserotationstyle: Shoemake``);
-it resembles the ``sphere`` style, but is free of hysteresis,
-i.e., returning mouse to the original position
-returns the figure to its original orientation; the rotation is independent
-of the details of the path the mouse took, which could be desirable.
-However, Shoemake's arcball rotates at twice the angular rate of the
-mouse movement (it is quite noticeable, especially when adjusting roll),
-and it lacks an obvious mechanical equivalent; arguably, the path-independent
-rotation is not natural (however convenient), it could take some getting used to.
-So it is a trade-off.
-
-Henriksen et al. [Henriksen2002]_ provide an overview. In summary:
+it resembles the ``sphere`` style, but has the benefit of being free of hysteresis,
+such that returning the mouse to the original position returns the figure to its
+original orientation. This path independence of the rotation has the nice property
+of being able to 'undo' an errant rotation. However, Shoemake's arcball rotates at
+twice the angular rate of the mouse movement (noticeable especially when adjusting
+roll), and it lacks an obvious mechanical equivalent; arguably, the path-independent
+rotation is not natural and it could take some getting used to.
+So there is a trade-off.
+
+Henriksen et al. [Henriksen2002]_ and Shambaugh [Shambaugh2024]_ provide
+overviews. In summary:
 
 .. list-table::
    :width: 100%
@@ -106,7 +105,7 @@ Henriksen et al. [Henriksen2002]_ provide an overview. In summary:
      - ❌
      - ✓ [6]_
      - ✔️
-     - ❌
+     - ✔️
      - ✔️
    * - sphere
      - ❌
@@ -127,7 +126,7 @@ Henriksen et al. [Henriksen2002]_ provide an overview. In summary:
 .. [3] Figure reacts the same way to mouse movements, regardless of orientation (no difference between 'poles' and 'equator')
 .. [4] Returning mouse to original position returns figure to original orientation (rotation is independent of the details of the path the mouse took)
 .. [5] The style has a corresponding natural implementation as a mechanical device
-.. [6] While it is possible to control roll with the ``trackball`` style, this is not immediately obvious (it requires moving the mouse in large circles) and a bit counterintuitive (the resulting roll is in the opposite direction)
+.. [6] While it is possible to control roll with the ``trackball`` style, this is not immediately obvious (it requires chaining multiple rotations together)
 
 You can try out one of the various mouse rotation styles using:
 
@@ -202,4 +201,8 @@ The border is a circular arc, wrapped around the arcball sphere cylindrically
   and Computer Graphics, Volume 10, Issue 2, March-April 2004, pp. 206-216,
   https://doi.org/10.1109/TVCG.2004.1260772 `[full-text]`__;
 
+.. [Shambaugh2024] Scott Shambaugh, "Virtual Trackballs: An Interactive
+  Taxonomy", 11 November 2024,
+  https://theshamblog.com/virtual-trackballs-a-taxonomy/
+
 __ https://www.researchgate.net/publication/8329656_Virtual_Trackballs_Revisited#fullTextFileContent
diff --git a/lib/mpl_toolkits/mplot3d/axes3d.py b/lib/mpl_toolkits/mplot3d/axes3d.py
@@ -1364,7 +1364,12 @@ def clear(self):
     def _button_press(self, event):
         if event.inaxes == self:
             self.button_pressed = event.button
-            self._sx, self._sy = event.xdata, event.ydata
+            self._sx0, self._sy0 = event.xdata, event.ydata
+            self._sx, self._sy = self._sx0, self._sy0
+            q0 = _Quaternion.from_cardan_angles(
+                *np.deg2rad((self.elev, self.azim, self.roll)))
+            self._q0 = q0
+
             toolbar = self.get_figure(root=True).canvas.toolbar
             if toolbar and toolbar._nav_stack() is None:
                 toolbar.push_current()
@@ -1566,6 +1571,7 @@ def _on_move(self, event):
             return
 
         dx, dy = x - self._sx, y - self._sy
+        dx0, dy0 = x - self._sx0, y - self._sy0
         w = self._pseudo_w
         h = self._pseudo_h
 
@@ -1589,19 +1595,22 @@ def _on_move(self, event):
                         *np.deg2rad((self.elev, self.azim, self.roll)))
 
                 if style == 'trackball':
-                    k = np.array([0, -dy/h, dx/w])
+                    # To avoid precession, we need to rotate relative to the
+                    # original orientation, not the current orientation.
+                    k = np.array([0, -dy0/h, dx0/w])
                     nk = np.linalg.norm(k)
                     th = nk / mpl.rcParams['axes3d.trackballsize']
                     dq = _Quaternion(np.cos(th), k*np.sin(th)/nk)
+                    q = dq * self._q0
                 else:  # 'sphere', 'arcball'
                     current_vec = self._arcball(self._sx/w, self._sy/h)
                     new_vec = self._arcball(x/w, y/h)
                     if style == 'sphere':
                         dq = _Quaternion.rotate_from_to(current_vec, new_vec)
                     else:  # 'arcball'
                         dq = _Quaternion(0, new_vec) * _Quaternion(0, -current_vec)
+                    q = dq * q
 
-                q = dq * q
                 elev, azim, roll = np.rad2deg(q.as_cardan_angles())
 
             # update view