<p>The chaotic dynamics of a rotation-invariant system in circuit systems is investigated analytically in this paper. Utilizing the generalized Hamilton principle, the system undergoes some transformations into a three-dimensional perturbed Hamiltonian system. The homoclinic and heteroclinic orbits for the systems are derived. Parameter expressions of six orbits for the degraded system without disturbance are derived and subsequently verified. The existence of perturbed homoclinic, heteroclinic, and periodic orbits within the system is rigorously proved, and explicit parametric conditions can be determined by the method of Melnikov vector. The critical surface demarcating the onset of chaos has been identified, and specific regions where chaos is likely to occur, as well as the modulus range encompassing subharmonic bifurcations are characterized. Ultimately, the route of the system into chaos via subharmonic bifurcations is analyzed and validated through numerical simulations.</p>