Jimbo, K. Souda, H. JACoW Geneva, Switzerland 978-3-95450-180-9 10.18429/JACoW-NAPAC2016-WEPOA03 English 690-692 WEPOA03 ion synchrotron betatron heavy-ion closed-orbit Contribution to a conference proceedings 2017 2017-01 http://dx.doi.org/10.18429/JACoW-NAPAC2016-WEPOA03 https://jacow.org/napac2016/papers/wepoa03.pdf The Hamiltonian, which was composed of coasting, synchrotron and betatron motions, clarified the synchro-betatron resonant coupling mechanism in a storage ring*. The equation for the synchrotron motion was also obtained from the Hamiltonian. It shows that the so-called synchrotron oscillation is an oscillation around the revolution frequency as well as of the kinetic energy of the on-momentum particle. The detectable synchrotron oscillation is a horizontal oscillation on the laboratory frame.