Newton’s \(2\textrm{nd}\) lawNewtonsecond law generally holds only inFrameinertial inertial frames of reference. However, there are physical situations where it is quite natural or necessary to study the equations of motion in a noninertial frameFramenoninertial. For instance, a frame that is attached to a rotating rigid body is noninertial. In Sect.  8.11 , we obtained Euler’s equations for the linear and angular momenta in such a corotating frame and found that they involve new terms \({\boldsymbol{\Omega }}\times {\boldsymbol{P}}\) and \({\boldsymbol{\Omega }}\times {\boldsymbol{L}}\) depending on the instantaneous angular velocity \({\boldsymbol{\Omega }}\) of the frame. Moreover, we found that it was conceptually and technically beneficial to first solve Euler’s equations in the corotating frame and then determine the orientation of the corotating frame relative to the lab frame. Another situation where the effects of a noninertial frame enter is in the motion of a simple pendulum where the Earth’s rotation makes the lab frame noninertial and can cause the pendulum’s oscillation plane to precess.

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Motion in Noninertial Frames of Reference

  • Govind S. Krishnaswami

摘要

Newton’s \(2\textrm{nd}\) lawNewtonsecond law generally holds only inFrameinertial inertial frames of reference. However, there are physical situations where it is quite natural or necessary to study the equations of motion in a noninertial frameFramenoninertial. For instance, a frame that is attached to a rotating rigid body is noninertial. In Sect.  8.11 , we obtained Euler’s equations for the linear and angular momenta in such a corotating frame and found that they involve new terms \({\boldsymbol{\Omega }}\times {\boldsymbol{P}}\) and \({\boldsymbol{\Omega }}\times {\boldsymbol{L}}\) depending on the instantaneous angular velocity \({\boldsymbol{\Omega }}\) of the frame. Moreover, we found that it was conceptually and technically beneficial to first solve Euler’s equations in the corotating frame and then determine the orientation of the corotating frame relative to the lab frame. Another situation where the effects of a noninertial frame enter is in the motion of a simple pendulum where the Earth’s rotation makes the lab frame noninertial and can cause the pendulum’s oscillation plane to precess.