4.3: Outline and elements of dynamics
Newton’s laws are based on the following elemental concepts.
Concept. Elements of dynamics
- Space - Every location in space is identified by a position vector \(\overrightarrow{\boldsymbol{r}}\).
- Time - Position vectors can change in time \(t\), such that there is motion.
- Mass - Objects can consist of one or more point masses \(i\), each having a well defined position vector \(\overrightarrow{\boldsymbol{r}}_{i}\) and mass \(m_{i}\).
- Force- On every point mass \(i\) one or more force vectors \(\overrightarrow{\boldsymbol{F}}_{i j}(t)\) can act.
In the following chapters we will discuss these elemental concepts in more detail to describe the dynamic motion of objects, and then continue to discuss how this motion is related to mass and force. The subject of dynamics can be described as follows.
Dynamics is the field of science and engineering concerned with predicting and analysing the motion \(\overrightarrow{\boldsymbol{r}}_{i}(t)\) of point masses under the influence of forces and constraints.
Since all matter in our universe consists of point masses, which are called elementary particles and move in response to four fundamental forces of nature, the field of dynamics covers practically all science with subdisciplines like classical dynamics, electrodynamics, quantum dynamics, and thermodynamics, but also chemistry and biology. In this textbook we will only discuss the dynamics that can be described by Newton’s laws, which is generally called classical dynamics. The field of dynamics can be split into two main domains:
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Kinematics
- Study of the motion of objects in space and time without considering the forces that cause this motion.
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Kinetics
- Study of the motion of objects in relation to mass and forces.
Figure 4.1 illustrates the roles of kinematics and kinetics in dynamics. Kinetics is used to relate the forces to the accelerations and equation of motion, while kinematics is used to relate the equations of motion (which are differential equations) and constraint equations to the actual motion. The figure illustrates that one can predict the motion \(\overrightarrow{\boldsymbol{r}}(t)\) at all times if the forces and initial conditions are known, and that it is also possible to determine the forces if the motion is known.
Besides the division into kinematics and kinetics, there is also a division of dynamics based on the types of objects that are being analysed:
- Point masses -Objects whose mass is located on a single point in space.
- Rigid bodies - Objects whose mass distribution in space is rigid and undeformable.
- Deformable bodies and fluids - Objects whose mass distribution in space is deformable like in elastic solids or can flow like a liquid or gas.
In part II we will discuss the dynamics of point masses, while in part III we will analyse the dynamics of rigid bodies. Deformable bodies are out of the scope of this textbook. For both parts we will discuss kinematics, kinetics, the method of work and energy and the method of impulse and momentum. Finally we will conclude with the discussion of vibrations. This division leads to the following outline of the rest of the chapters of this textbook:
- Kinematics of point masses: Ch. 5
- Kinetics of point masses: Ch. 6
- Work and energy of point masses: Ch. 7
- Impulse and momentum of point masses: Ch. 8
- Kinematics of rigid bodies: Ch. 9
- Kinetics of rigid bodies: Ch. 10
- Work and energy of rigid bodies: Ch. 11
- Impulse and momentum of point masses: Ch. 12
- Vibrations of point masses and rigid bodies: Ch. 13
- Solution strategy dynamics: Ch. 14
- Bibliography: Ch. 15