Rule 12 of 36 · Chapter II — Symmetry & Conservation
Look first for what stays the same
Why this rule exists
Most of what happens in a physical process is complicated and irrelevant; the invariants are where the physics is. Looking first for what stays the same inverts the usual approach and pays off, because a conserved or unchanging quantity gives an equation valid at every instant, sidestepping the detailed evolution entirely. This is why symmetry and conservation arguments so often reach the answer in a line where brute-force integration takes a page.
In practice
Before writing any equation of motion, scan for invariants: total energy, momentum, angular momentum, charge, but also anything the problem's structure holds fixed — a ratio, a center of mass, a quantity two effects trade between. Each invariant is a conserved-total equation you can write down immediately. Often enough of them determine the answer with no dynamics at all; only when invariants run out do you fall back to solving the motion step by step.
When it doesn't apply
Some quantities appear constant only within an approximation and drift once you look closer or wait long enough — adiabatic invariants hold while conditions change slowly, not exactly. And strongly dissipative or driven systems may conserve little, so the search for invariants comes up empty and dynamics is unavoidable.