My brain eventually suggested that 'dynamic' refers to something changing (i.e. non-static), while 'dynamical' refers to something involving dynamics. Searching along these lines, I think this answer really hits it (english.stackexchange.com/a/31650/23771). To motivate the need, or validity, of this distinction, consider a typical (scientific) example,

'Dynamical Friction' is a process in astrophysics where an effective friction force (i.e. one which is dissipative) is generated by motion in a dense medium. The requirement of motion means the system is 'dynamic', while the resulting friction force could be completely constant in time and space---and thus, is itself not dynamic, but instead dynamical.


An answer given here explains the difference:

dynamic: characterized by action or forcefulness or force of personality; "a dynamic market"; "a dynamic speaker"; "the dynamic president of the republic"

dynamical: refers to specific systems that change over time or dimension A dynamical systems is a mathematical formalization for any fixed "rule" which describes the time dependence of a point's position in its ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each spring in a lake.

An additional explanation is given that "dynamic" means forceful or powerful, and "dynamical" relates to the mathematical subject of dynamics.