Kinetics (technical mechanics)

The kinetics in technical mechanics
Technical mechanics                                                           Statics   dynamics   Strength theory                                             kinematics   kinetics

The kinetics ( Greek kinesis , movement ') is a branch of engineering mechanics and describes the change in the movement parameters ( location , velocity , and acceleration ) under the action of forces , taking into account also the mass of the moving body. The kinematics contrast, describes the motion of a body (position, velocity, acceleration) without forces or masses to be considered.

Technical mechanics is usually divided into the three areas of statics , strength theory and dynamics, which then consist of the two sub-areas of kinetics and kinematics. In physics , on the other hand, mechanics are divided into kinematics and dynamics, which there contain statics and kinetics. In this sense, the term was coined in 1879 by William Thomson, 1st Baron Kelvin and Peter Guthrie Tait in their treatise on Natural Philosophy .

Important rates of kinetics

Using the theorems of kinetics, the equation of motion of a system can be set up depending on the freely selectable generalized coordinates .

Center of gravity or momentum theorem

The so-called basic law of dynamics, Newton's second law (also called the law of momentum ), is one of the best-known laws of dynamics .

${\displaystyle {\vec {F}}=m\cdot {\vec {a}}_{\mathrm {s} }}$.

Where the force, m is the mass and the acceleration. ${\displaystyle {\vec {F}}}$ ${\displaystyle {\vec {a}}_{\mathrm {s} }}$

This equation only applies to a mass m that is constant over time . For the general case of a time-varying mass, the force must be defined as the time derivative of the momentum : ${\displaystyle {\vec {p}}=m{\vec {v}}}$

${\displaystyle {\vec {F}}={\frac {\mathrm {d} {\vec {p}}}{\mathrm {d} t}}={\frac {\mathrm {d} }{\mathrm {d} t}}(m{\vec {v}})=m{\frac {\mathrm {d} {\vec {v}}}{\mathrm {d} t}}+{\frac {\mathrm {d} m}{\mathrm {d} t}}{\vec {v}}}$.

There is speed. The second part, for example, as the product of mass flow and speed, mediates the flow of force between an aircraft and the ground, see momentum flow in dynamic lift . ${\displaystyle {\vec {v}}}$

Performance rate

The principle of performance of mechanics can also be used to describe non-conservative systems with one degree of freedom.

Energy law

The energy law of mechanics follows as a special case from the power law for conservative systems.

Working set

The working set

${\displaystyle W=\int _{\gamma }F\mathrm {d} s}$

finally forms the fourth possibility to determine the equation of motion of a dynamic system. With the work W , kinetic energy is fed to the body on which the force F acts along the path γ , which can then be converted into position energy or deformation energy according to the law of conservation of energy . Energy is withdrawn from the force-exerting system in the same way as it is transmitted through work.

literature

• R. Mahnken: Textbook of Technical Mechanics - Dynamics . 2nd edition Springer, Berlin 2012, ISBN 978-3-642-19837-3
• RC Hibbeler: Technical Mechanics 3 - Dynamics. 10th edition, Pearson Studium, Munich 2006, ISBN 3-8273-7135-X
• Alfred Böge: Technical mechanics - statics, dynamics, fluid mechanics, strength theory. 27th edition, ISBN 3-8348-0115-1
• Dietmar Gross, Werner Hauger, Jörg Schröder, Wolfgang A. Wall: Technical Mechanics: Volume 3: Kinetics . 12th edition. Springer Vieweg, 2012, ISBN 978-3-642-29529-4 .

Web links

Wikibooks: Dynamics  - Learning and Teaching Materials

Individual evidence

1. ↑ Mahnken: Textbook of Technical Mechanics - Dynamics , Springer, 2nd edition, 2012, p. 3.
2. ^ Günter Holzmann, Heinz Meyer, Georg Schumpich: Technical Mechanics Statics . 12th edition. S. 2 .
3. ↑ Lord Kelvin , Peter Guthrie Tait : Treatise on Natural Philosophy . Part I. Cambridge University press, London, Berlin, New York 1912, pp. vi ( archive.org [accessed December 13, 2017] first edition 1879, reprint 1886, 1890, 1896, 1903 and 1912).
4. ^ Gross, Hauger, Schröder, Wall (2012), p. 65.