14.2: Flowchart kinematics
Go to 18: determine forces and moments from \(\overrightarrow{\boldsymbol{a}}\) and \(\overrightarrow{\boldsymbol{\alpha}}\)
- This flowchart shows the strategy for dealing with kinematics problems.
- First determine if we deal with a rigid body or point mass, since the kinematics of point masses is significantly simpler.
- Kinematics translation: the goal is to determine position \(\overrightarrow{\boldsymbol{r}}\), velocity \(\overrightarrow{\boldsymbol{v}}\) and acceleration \(\overrightarrow{\boldsymbol{a}}\) if only one of the three is known. This is done by solving the ODE, e.g. by differentiation and integration over time \(t\), or along the path \(s\) or angle \(\phi\) coordinate (see Table 5.1). In 3D we have derived equations to differentiate along Cartesian, natural or cylindrical coordinates (
- Rotating coordinate systems: the goal is to determine \(\overrightarrow{\boldsymbol{v}}_{B}, \overrightarrow{\boldsymbol{a}}_{B}\) of point \(B\) in an IRF if \(\overrightarrow{\boldsymbol{v}}_{B}^{\prime}\) and \(\overrightarrow{\boldsymbol{a}}_{B}^{\prime}\) are known in a CS that rotates with angular velocity \(\overrightarrow{\boldsymbol{\Omega}}\), or vice versa (see Sec. 9.7).
- Rotating rigid bodies: the goal is to determine \(\overrightarrow{\boldsymbol{v}}_{B}, \overrightarrow{\boldsymbol{a}}_{B}\) of a point \(B\) that is fixed on a rigid body if \(\overrightarrow{\boldsymbol{\omega}}\) and \(\overrightarrow{\boldsymbol{\alpha}}\) are known or vice versa. Translation of a point is dealt with similar as in step 13. The kinematic equations for rotation of rigid body are discussed in Ch. 9. In particular the instantaneous centre of rotation (IC, see Sec. 9.5.1) can facilitate determination of velocities.
- The kinematic equations are determined using steps 13-15.
- Finally the motion \(\overrightarrow{\boldsymbol{r}}(t), \overrightarrow{\boldsymbol{v}}, \overrightarrow{\boldsymbol{a}}, \overrightarrow{\boldsymbol{\omega}}, \overrightarrow{\boldsymbol{\alpha}}\) is determined by solving the kinematic and constraint (differential) equations. In case one needs to determine forces: go to step 18 to achieve this with kinetics.