Solinger A B
Department of Research, Life Chiropractic College West, Hayward, CA, USA.
J Manipulative Physiol Ther. 1996 Jan;19(1):26-31.
To rigorously develop the physics and mathematics of the model of spinal manipulative therapy (SMT) consisting of a damped linear oscillator representing the vertebra impacted by a spring system representing the doctor, to interpret the results and to compare and contrast them with an earlier similar study originally developed in approximation.
Mathematical physics analysis.
Careful consideration of the exact equations and their meaning leads one to eliminate as unnecessary the picture of the doctor as a spring system, replacing it with the force function, which represents the applied SMT thrust as a function of time. Thus, with correct application of the principles of physics to the original model, one is led directly to a linear harmonic oscillator model for the vertebral system, with a forcing function for the SMT thrust and possible preload. The details of the application of such a model are developed elsewhere.
The distraction resultant from an SMT thrust is shown to be a function of the momentum transfer, not, as asserted by the originator of the model, the velocity. The quickness of the application of the SMT thrust must be measured relative to normal mode frequencies of the spine. Further detailed examination of the physics of the model leads one to modify or contradict several other conclusions of the model's originator. Most importantly, the fact that the details of the physics of this model can be worked out analytically (as opposed to having to employ numerical methods) holds out the promise of additional insights to be gained by further development of this approach.
严谨地推导脊柱手法治疗（SMT）模型的物理和数学原理。该模型由一个阻尼线性振荡器代表椎骨，一个弹簧系统代表医生对椎骨施加冲击，对结果进行解释，并将其与早期一个近似开发的类似研究进行比较和对比。
数学物理分析。
仔细考虑精确的方程及其含义后，人们发现将医生视为弹簧系统的描述是不必要的，可以用一个力函数来替代，该力函数将施加的SMT推力表示为时间的函数。因此，通过正确地将物理原理应用于原始模型，人们直接得到了一个用于脊柱系统的线性谐波振荡器模型，该模型具有SMT推力的强迫函数和可能的预载。这种模型的应用细节在其他地方有阐述。
SMT推力产生的牵张被证明是动量传递的函数，而不是如该模型创始人所断言的速度的函数。SMT推力的施加速度必须相对于脊柱的正常模式频率来衡量。对该模型物理原理的进一步详细研究导致人们对该模型创始人的其他几个结论进行修改或提出质疑。最重要的是，这个模型的物理细节可以通过解析方法得出（而不必采用数值方法），这为通过进一步发展这种方法获得更多见解带来了希望。
