Artificial classical wave systems such as wave crystals and metamaterials have demonstrated promising capabilities in simulating a wide range of quantum mechanical phenomena. Yet some gaps between quantum and classical worlds are generally considered fundamental and difficult to bridge. Dynamics obeying special unitary groups, e.g., electronic spins described by SU(2), color symmetries of fundamental particles described by SU(3), are such examples. In this Letter, we present the experimental realization of universal SU(2) and SU(3) dynamic operations in classical mechanical oscillator systems with temporally modulated coupling terms. Our approach relies on the sequential execution of nonadiabatic holonomic evolutions, which are typically used in constructing quantum-logic gates. The method is swift and purely geometric and can be extended to realize more sophisticated dynamic operations. Our results open a new way for studying and simulating quantum phenomena in classical systems.

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• Classical mechanics
• Quantum simulation
• SU(N) symmetries