A model of the interaction of a spherical gas bubble and a rigid particle is derived as a coupled system of second-order differential equations using Lagrangian mechanics. The model takes into account oscillations of the bubble surface and the attached to it solid cylindrical particle in infinite volume of ideal incompressible liquid. The capillary force holding the particle on the bubble is due to the shape of the meniscus surface, which determines the wetting edge angle. The series with respect Legendre polynomials is used to present small axisymmetric oscillations of the particle-bubble system. Potential and kinetic energies are expressed through coefficients of this series. Particle adhesion condition to bubble surface is implemented through Lagrange multipliers. The dependence of the particle size and its density is demonstrated as a result of the numerical integration of the resulting dynamic system of differential equations.

使用拉格朗日力学将球形气泡和刚性粒子的相互作用模型导出为二阶微分方程的耦合系统。该模型考虑了在无限体积的理想不可压缩液体中气泡表面和附着在其上的固体圆柱形颗粒的振荡。将颗粒保持在气泡上的毛细力是由于弯液面的形状，它决定了润湿边缘的角度。关于勒让德多项式的级数用于呈现粒子-气泡系统的小轴对称振荡。势能和动能通过该系列的系数表示。粒子对气泡表面的粘附条件是通过拉​​格朗日乘子实现的。