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A contribution to calculation of the mathematical pendulum

机译:对数学摆的计算的贡献

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In this work, as a continuation of rigorous solutions of the mathematical pendulum theory, calculated dependences were obtained in elementary functions (with construction of plots) for a complete description of the oscillatory motion of the pendulum with determination of its parameters, such as the oscillation period, deviation angles, time of motion, angular velocity and acceleration, and strains in the pendulum rod (maximum, minimum, zero, and gravitational). The results of calculations according to the proposed dependences closely (a parts per thousand(a)1%) coincide with the exact tabulated data for individual points. The conditions of ascending at which the angular velocity, angular acceleration, and strains in the pendulum rod reach their limiting values equal to and 5m (1) g, respectively, are shown. It was revealed that the angular acceleration does not depend on the pendulum oscillation amplitude; the pendulum rod strain equal to the gravitation force of the pendulum R (s) = m (1) g at the time instant is also independent on the amplitude. The dependences presented in this work can also be invoked for describing oscillations of a physical pendulum, mass on a spring, electric circuit, etc.
机译:在这项工作中,作为数学摆理论的严格解的延续,在基本函数中获得了计算的依存关系(通过构建图),以完整描述摆的振荡运动并确定其参数,例如振荡周期,偏差角,运动时间,角速度和加速度以及摆杆中的应变(最大,最小,零和重力)。根据建议的依赖性的计算结果紧密相关(千分之一(a)1%),与各个点的精确列表数据一致。示出了在上升条件下,摆杆中的角速度,角加速度和应变分别达到等于和等于5m(1)g的极限值。结果表明,角加速度不依赖于摆振动幅度。摆杆应变等于摆锤的重力R(s)= m(1)g,在瞬间也与振幅无关。也可以引用此工作中呈现的相关性来描述物理摆,弹簧上的质量,电路等的振动。

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