Abstract The resolution of the acceleration vector of a particle moving along a space curve is well known thanks to Siacci [1]. This resolution comprises two special oblique components which lie in the osculating plane of the curve. The jerk is the time derivative of acceleration vector. For the jerk vector of the aforementioned particle, a similar resolution is presented as a new contribution to field [2]. It comprises three special oblique components which lie in the osculating and rectifying planes. In this paper, we have studied the Siacci’s resolution of the acceleration vector and aforementioned resolution of the jerk vector for the space curves which are equipped with the modified orthogonal frame. Moreover, we have given some illustrative examples to show how the our theorems work.

中文翻译：

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关于沿空间曲线运动的加速度和加加速度的注记

摘要 由于 Siacci [1]，粒子沿空间曲线运动的加速度矢量的分辨率是众所周知的。该分辨率包括位于曲线密切平面内的两个特殊倾斜分量。加加速度是加速度矢量的时间导数。对于上述粒子的加加速度矢量，类似的分辨率被呈现为对场的新贡献 [2]。它包括三个特殊的倾斜分量，它们位于密切平面和整流平面中。在本文中，我们研究了配备修正正交坐标系的空间曲线的加速度矢量的 Siacci 分辨率和上述加加速度矢量的分辨率。此外，我们给出了一些说明性的例子来展示我们的定理是如何工作的。