OSCILLATION OF A MATHEMATICAL PENDULUM TAKING INTO ACCOUNT GLOBE ROTATION

Abstract

Purpose. Development of mathematical pendulum model which considers rotation of globe roundit’s own axis and parallel at which pendulum has been installed with use of Lagrange’s differential equations of the second kind. Checking whether oscillation plane position with respect to a meridian influences mathematical pendulum model. Methods of research. Mathematical modelling, Lagrange’s differential equations of the second kind. Results. Two design schemes of a mathematical pendulum have been developed which consider rotation of globe roundit’s own axis and pendulum installation place. They differ only by oscillation plane position with respect to a meridian. Formulas for kinetic energy for both schemes and the general formula for potential energy have been developed. The corresponding nonlinear differential equations are received by means of Lagrange’s differential equations of the second kind. The analysis of the received results show, that oscillation period of a mathematical pendulum depends not only on amplitude but as well on parallel at which the the test has been executed, and also oscillation plane position with respect to a meridian. Scientific novelty. The model of a mathematical pendulum has been developed with use of Lagrange’s differential equations of the second kind, which considers rotation of globe roundit’s own axis and pendulum installation place. Practical value.It’s found out, that not only amplitude, but position of oscillation plane with respect to a meridian, and also a parallel at which the the test has been executed influences mathematical pendulum oscillation. In particular, it has essential value when search of minerals is carried out by means of gravimetry using pendular devices, when smallest changes of a gravitational constant are estimated.