On the stability of the equilibrium state of a rigid body with a multilayer ideal fluid separated by elastic plates

• Date: 2026
• Main Authors: Kononov, Yu. M., Юрій Микитович Кононов, Юрий, Кононов, Ю. М.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2026
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/6840
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 531.36:531.38:533.6.013.42L. N. Stretensky’s problem and the problem of physical pendulum oscillations are generalized to the case of a multilayer ideal fluid separated by elastic plates. Assuming the positive definiteness of the potential energy (L. N. Stretensky’s problem) and changed potential energy (the physical pendulum), we obtain the conditions of stability for the equilibrium state in these problems. A more detailed study is performed in the case of a cylindrical cavity of arbitrary cross-section. We show that for the stability of the equilibrium state in L. N. Stretensky’s problem it is necessary and sufficient that there exists a stable equilibrium state of the elastic plates and liquid in the stationary rigid body and it is sufficient that a heavier liquid is located below a lighter one. For the stability of the equilibrium state in the problem of physical pendulum oscillations, it is also necessary that there is a stable equilibrium state of the elastic plates and liquid in the stationary rigid body.It is also shown that we can use pre-tensioning of plates to stabilize an unstable equilibrium position of the physical pendulum.