Chapter 2
Stress and Strain in Continuum
2.1 Newton’s Universal Laws of Motion
It is essential to start the discussion about continuum mechanics with universal laws of
motion as given by Newton. Understanding their implications in historical context is
essential to understand these simple and probably most famous physics equations Of
course, Newton’s universal laws of motion are very well-known to most readers of this
book; however, their historical context and derivations are not. Therefore, we find it
necessary to quote these basics from Sir Isaac Newton’s own Wikipedia web site with
their sources. The information below is quoted directly with little or no editing.
Philosophiæ Naturalis Principia Mathematica (Latin for Mathematical Principles of Natural Philosophy) (Newton n.d.-a), often referred to as simply the
Principia, is a work in three books by Isaac Newton, in Latin, first published on
5 July 1687. After annotating and correcting his personal copy of the first edition
(Newton n.d.-a), Newton published two further editions, in 1713 and 1726 (Harvard
UP 1972). The Principia states Newton’s laws of motion, forming the foundation of
classical mechanics, Newton’s law of universal gravitation, and a derivation of
Kepler’s laws of planetary motion (which Kepler first obtained empirically) (Anon
2020; Cohen 2002; Galili and Tseitlin 2003; Kleppner and Kolenkow 1973; Plastino
and Muzzio 1992; Halliday et al. 1992) (Fig. 2.1).
2.1.1 First Universal Law of Motion
Original text in Latin reads:
Newton’s original Latin text in Principia states:
“ Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in
directum, nisi quatenus a viribus impressis cogitur statum illum mutare.”
Translated to English, this reads:
© Springer Nature Switzerland AG 2021
C. Basaran, Introduction to Unified Mechanics Theory with Applications,
https://doi.org/10.1007/978-3-030-57772-8_2
5
Stress and Strain in Continuum
2.1 Newton’s Universal Laws of Motion
It is essential to start the discussion about continuum mechanics with universal laws of
motion as given by Newton. Understanding their implications in historical context is
essential to understand these simple and probably most famous physics equations Of
course, Newton’s universal laws of motion are very well-known to most readers of this
book; however, their historical context and derivations are not. Therefore, we find it
necessary to quote these basics from Sir Isaac Newton’s own Wikipedia web site with
their sources. The information below is quoted directly with little or no editing.
Philosophiæ Naturalis Principia Mathematica (Latin for Mathematical Principles of Natural Philosophy) (Newton n.d.-a), often referred to as simply the
Principia, is a work in three books by Isaac Newton, in Latin, first published on
5 July 1687. After annotating and correcting his personal copy of the first edition
(Newton n.d.-a), Newton published two further editions, in 1713 and 1726 (Harvard
UP 1972). The Principia states Newton’s laws of motion, forming the foundation of
classical mechanics, Newton’s law of universal gravitation, and a derivation of
Kepler’s laws of planetary motion (which Kepler first obtained empirically) (Anon
2020; Cohen 2002; Galili and Tseitlin 2003; Kleppner and Kolenkow 1973; Plastino
and Muzzio 1992; Halliday et al. 1992) (Fig. 2.1).
2.1.1 First Universal Law of Motion
Original text in Latin reads:
Newton’s original Latin text in Principia states:
“ Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in
directum, nisi quatenus a viribus impressis cogitur statum illum mutare.”
Translated to English, this reads:
© Springer Nature Switzerland AG 2021
C. Basaran, Introduction to Unified Mechanics Theory with Applications,
https://doi.org/10.1007/978-3-030-57772-8_2
5