Why is a dynamical system not a dynamic system?
Thing is, they do not mean the same thing. At least, not in theory.
Dynamic the adjective means "exhibiting continual change".
Dynamics the noun means "the study of forces and their relation to motion".
Dynamical the adjective means "relating to the study of dynamics."
A "dynamic" system is a system exhibiting continual change. A "dynamical" system is a system relating to the study of dynamics. (Since OP is Chinese, this is also why DS is 動力系統 and not 不定系統.)
Similarly,
Tangent the adjective means the geometric notion of touching but not intersecting.
Tangent the noun refers first to the geometric construct of the line tangent to a shape, and then also to the idea of "objects that can be split off without making a turn", whence the idea of "going on a tangent" when you derail the discussion with something related but not directly relevant. (You won't be going on a tangent if you change the topic or the direction of discussion abruptly.)
Tangential the adjective refers to the quality of "tangent". Hence you make a "tangential remark" while you "go on a tangent". Hence you look for "tangent lines" while compute "tangential forces". (The force itself is not tangent, but it is directly along the line that is tangent to the object.)
This, of course, gets muddled by the fact that English is perfectly happy with attributive nouns. English being remarkably loosey goosey about grammar for a Western language, understanding in theory why things are the way they are is probably much less useful than accepting their use as a convention. (After all, what is language but a convention to enable communication?)
Homework exercise: discuss transverse versus transversal
Here are the two entries from Anthony Lo Bello's Origins of Mathematical Words (John Hopkins, 2013) which is very informative, entertaining, and perhaps curmudgeonly. In his parlance, following the lexicographer Samuel Johnson, a "low word" is one with an "irregular combination" of roots that has "little or no etymological legitimacy."
dynamical The Greek noun [dunamis] means power. The corresponding Greek adjective is [dunamikos], pertaining to power. The correct English adjective is therefore dynamic. To superimpose the vestige -al of the Latin adjectival ending -alis upon the stem of a Greek adjective is often the product of ignorance and produces a low word. In other cases, the addition of the Latin suffix to the Greek adjective is due to the fact that a different meaning is intended from that of the Greek adjective; thus, dynamic was an established word, so one spoke of dynamical systems rather than dynamic systems to avoid confusion.
tangential See the entry tangent. The Latin adjectival suffix -alis was added to the stem of the participle tangens, tangentis, which was already an adjective but felt to be a noun, the tangent.
Early uses of "dynamical" go back to the 19th century at least:
On a dynamical theory of gratings, Lord Rayleigh (1907)
On the dynamical theory of gases, J.C. Maxwell (1865)
Thermo-dynamical as an adjective was also common, see for example W. Gibbs's Thermodynamical Model (1900).