14.3: Flowchart kinetics
- Kinetics is used to determine the equation of motion from the forces and Newton’s and Euler’s laws.
- The first step is to cut objects with mass loose and draw an FBD for each of them (see Sec. 6.8 ).
- Use the FBD to determine the sum of forces and sum of moments, and project them on the coordinate system.
- Determine the centre of mass CoM (see Sec. 7.3.2) and moment of inertia \(I_{G}\) of each object (see Sec. 10.5).
- The kinetic analysis can be significantly simplified by using the method of work and energy or the method of (angular) impulse and momentum, so carefully choose the right method.
- Work and energy can be used if (see Ch. 7 and Ch. 11)
- Forces as a function of position \(\overrightarrow{\boldsymbol{F}}(\overrightarrow{\boldsymbol{r}})\) or moments as function of angle are known.
- The trajectory/path is known or does not need to be determined.
- There is only 1 unknown scalar (e.g. the final speed).
Conservation of energy can further simplify the analysis if all forces are conservative forces.
- (Angular) impulse and momentum can be used if (see Ch. 8 and Ch. 12):
- Impulse and/or angular impulse by external forces can be determined.
- Only changes in (angular) velocity need to be determined, while the positions are approximately constant.
- In case the sum of external forces and/or moments is zero the analysis can be further simplified using conservation of momentum and/or angular momentum.
- Besides (angular) momentum conservation, energy conservation or coefficients of restitution can be used to solve e.g. collision problems.
- Equations of motion. Determine the equations of motion for translation and rotation using Euler’s laws and project them on the CS to obtain scalar equations (see Ch. 6 and Ch. 10). Combine them with the constraint equations. Note that solving these equations is mostly a mathematical and kinematics challenge.
- Solve the (differential) equations of motion to obtain the motion \(\overrightarrow{\boldsymbol{r}}(t)\). Go to step 11 to determine motion of all points using kinematics.
- Vibrations are special EoMs that are solved by special means for driven and free vibrations that can be damped or undamped (see Ch. 13).