The adjective 'dynamical' is widely used in astronomy, perhaps science in general, but it seems like it has the exact same meaning and usage as 'dynamic', and further, seems to be the same part of speech. Is this even real word? Should it have particular uses? Should it be not allowed to play with other words?
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.