Abstract
Some of the deepest concepts in science include the nature of motion and space. From the very beginning of modern science, the matter has been examined by many great scientists and thinkers.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
By Leibniz.
- 2.
Actually, this is the gravitational mass.
- 3.
In fact, Newton did not formulate his law of universal gravitation in the familiar form.
- 4.
This can be demonstrated in a more direct way using the laws of Galilean transformation. Let x–y–z be two inertial frames with the following transformation equations \(\varvec{r}^{\prime } = \varvec{r} - \varvec{u}t,\) \(\varvec{v}^{\prime } = \varvec{v} - \varvec{u},\) \(\varvec{a}^{\prime } = \varvec{a},t^{\prime } = t\); then, the following equalities are obtained: \(\varvec{r}_{1}^{\prime } - \varvec{r}_{2}^{\prime } = \varvec{r}_{1} - \varvec{r}_{2}\) and \(\varvec{v}_{1}^{\prime } - \varvec{v}_{2}^{\prime } = \varvec{v}_{1} - \varvec{v}_{2}\); and so, \(\frac{{{\text{d}}U}}{{{\text{d}}t}} = f\left( {\left| {\varvec{r}_{1} - \varvec{r}_{2} } \right|} \right)\left( {\varvec{r}_{1} - \varvec{r}_{2} } \right) \cdot \left( {\varvec{v}_{1} - \varvec{v}_{2} } \right) =\) \(f\left( {\left| {\varvec{r}_{1}^{\prime } - \varvec{r}_{2}^{\prime } } \right|} \right)\left( {\varvec{r}_{1}^{\prime } - \varvec{r}_{2}^{\prime } } \right) \cdot \left( {\varvec{v}_{1}^{\prime } - \varvec{v}_{2}^{\prime } } \right) = \frac{{{\text{d}}U^{\prime } }}{{{\text{d}}t}}\).
- 5.
Also spelled as ‘ether’.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Ghosh, A. (2018). Some Basic Concepts in Newtonian Mechanics. In: Conceptual Evolution of Newtonian and Relativistic Mechanics. Undergraduate Lecture Notes in Physics. Springer, Singapore. https://doi.org/10.1007/978-981-10-6253-7_2
Download citation
DOI: https://doi.org/10.1007/978-981-10-6253-7_2
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-6252-0
Online ISBN: 978-981-10-6253-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)