E289 -- Theoria motus corporum solidorum seu rigidorum
(Theory of the motion of solid or rigid bodies)
Originally published with the full title: Theoria motus corporum solidorum seu rigidorum ex primis nostrae cognitionis principiis
stabilita et ad omnes motus, qui in hujusmodi corpora cadere possunt, accommodata. Auctore
Leonh. Eulero academiae regiae scient. Borussicae directore academiae imper. Petropol. socio honorario et academiarum scient. regiarum Parisinae et Londinensis membro. Rostochii et
Gryphiswaldiae litteris et impensis A. F. Röse. MDCCLXV.
Summary:
After the “Praefatio” (see below) comes “Introductio
continens illustrationes et additiones necessarias de motu punctorum” in 6 chapters:
-
Consideratio motus in genere.
- De internis motus principiis.
- De causis motus externis seu
viribus.
- De mensuris absolutis ex lapsu gravium petitis.
- De motu absoluto corpusculorum a
viribus quibuscunque actorum.
- De motu respectivo corpusculorum, a viribus quibuscunque
sollicitatorum.
Then the main section “Tractatus de motu corporum rigidorum” follows in 19
chapters:
- De motu progressivo corporum rigidorum.
- De motu gyratorio circa axem fixum a
nullis viribus turbato.
- De motus gyratorii generatione.
- De perturbatione motus gyratorii a
viribus quibuscunque orta.
- De momento inertiae.
- Investigatio momenti inertiae in
corporibus homogeneis.
- De motu oscillatorio corporum gravium.
- De axe gyrationis libero
motuque corporum rigidorum circa tales axes.
- De prima motus generatione in corporibus
rigidis.
- De variatione momentanea axia gyrationis a viribus producta.
- De motu libero
corporum rigidorum ternis axibus principalibus paribus praeditorum et a nullis viribus
sollicitatorum.
- De motu libero corporum rigidorum duobus axibus principalibus paribus
praeditorum et nullis viribus sollicitatorum.
- De motu libero corporum rigidorum ternis
axibus principalibus disparibus praeditorum et nullis viribus sollicitatorum.
- De motu
turbinum super plano horizontali, in quibus omnia momenta inertiae sunt inter se aequalia.
-
De motu libero corporum rigidorum a viribus quibuscunque sollicitatorum.
- De motu
gyratorio seu vertiginis corporum coelestium.
- Plenior explicatio motus turbinum super plano
horizontali, semota frictione.
- De motu corporum basi sphaerica praeditorum super plano
horizontali.
- De motu corporum cylindricorum super plano horizontali.
At the end a
“Supplementum de motu corporum rigidorum a frictione perturbato” is found with 5 chapters:
-
De frictione in genere.
- De motu progressivo corporum gravium a frictione impedito.
- De
motu gyratorio corporum gravium circa axem fixum a frictione retardato.
- De motu turbinum
in cuspidem desinentium super plano horizontali, frictionis habita ratione.
- De motu globorum
centrum inertiae in ipsorum centro situm habentium super plano horizontali.
Publication:
-
Originally published as a book in 1765
-
Opera Omnia: Series 2, Volume 3, pp.
Documents Available:
- Because of the large size of this book, the original document version of E289
is presented here in nine parts:
- Ian Bruce has translated this book into English; the translation is available here.
- The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E289 include:
- de Boer R., “Theory of porous media - past and present.” Zeitschrift fur Angewandte Mathematik und Mechanik, 78 (7), pp. 441-466 (1998).
- Brush SG., “19th-century debates about the inside of the earth - solid, liquid or gas.” Annals of Science, 36 (3), pp. 225-254 (1979).
- A Detailed discussion of E289 can be found in:
          Speiser D., “The Kepler problem from Newton to Johann Bernoulli.” Archive for History of Exact Sciences, 50 (2), pp. 103-116 (1996).
- Malykin GB, Kharlamov SA., “Topological phase in classical mechanics.” Physics-Uspekhi, 46 (9), pp. 957-965 (Oct 2003).
- Moffatt HK., “Euler's disk and its finite-time singularity - air viscosity makes the rolling speed of a disk go up as its energy goes down.” Nature, 404 (6780), pp. 833-834 (Apr 20 2000).
- Steen LA., “Highlights in history of spectral theory.” American Mathematical Monthly, 80 (4), pp. 359-381 (1973).
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