Über die periodischen Lösungen der van der Polschen Differentialgleichung % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qaceWG4bGbamaacqGHRaWkcqaH8oqBdaqadaWdaeaapeGaamiEa8aa % daahaaWcbeqaa8qacaaIYaaaaOGaeyOeI0IaaGymaaGaayjkaiaawM % caaiqadIhagaGaaiabgUcaRiaadIhacqGH9aqpcaaIWaaaaa!43B7!:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | German |
| Veröffentlicht: |
Wiesbaden
VS Verlag für Sozialwissenschaften
1964
|
| Schriftenreihe: | Forschungsberichte des Landes Nordrhein-Westfalen
1307 |
| Schlagworte: | |
| Online-Zugang: | FLA01 Volltext |
| Beschreibung: | Probably it is not an exaggeration to say that, since the time of GALILEO who introduced the concept of the harmonic oscillator, we were able to actually ob serve a practically perfect physical image of the latter only when the VAN DER POL oscillator became available relatively a short time ago. In fact, very likely, there exists no better physical image of a simple harmonic motion than that which is produced by modern high quality electron tube oscillators, particulary those whose frequency is stabilized by quartz units. But this almost perfect physical image contains a germ of immense complexity due to the presence of an infinite spectrum of frequencies with which the energy fluctuates between the oscillator and the source of energy. These fluctuations escape our observation, however, if iJ. is very small . . . However, it is precisely this hidden complexity of vanishingly small energy fluctuations which permits obtaining a simple harmonie oscillation in its apparently pure form. N. MINORSKY, Energy Fluctuations 1D a VAN DER POL Oscillator, Journal of the Franklin Intitute 248 (1949). Diese Worte MINORSKYS stellen wir voran, um ein Schlaglicht auf die Bedeutung der v AN DER POLS ehen Differentialgleichung zu werfen. Wir verzichten hier darauf, physikalische und technische Einzelheiten näher auszuführen. Beispiele für V orgänge, die die v AN DER POLsehe Differentialgleichung beschreibt, finden sich in der angegebenen Literatur. Schon die Vielzahl der Vorgänge, die der v AN DER POLS ehen Differentialgleichung gehorchen, rechtfertigt ihr genaues Studium |
| Beschreibung: | 1 Online-Ressource (61 S.) |
| ISBN: | 9783322986269 9783322980038 |
| DOI: | 10.1007/978-3-322-98626-9 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-322-98626-9 |
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| id | DE-604.BV042461259 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:22:25Z |
| institution | BVB |
| isbn | 9783322986269 9783322980038 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027896466 |
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| publishDate | 1964 |
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| series2 | Forschungsberichte des Landes Nordrhein-Westfalen |
| spelling | Mankopf, Jürgen Richard Verfasser aut Über die periodischen Lösungen der van der Polschen Differentialgleichung % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qaceWG4bGbamaacqGHRaWkcqaH8oqBdaqadaWdaeaapeGaamiEa8aa % daahaaWcbeqaa8qacaaIYaaaaOGaeyOeI0IaaGymaaGaayjkaiaawM % caaiqadIhagaGaaiabgUcaRiaadIhacqGH9aqpcaaIWaaaaa!43B7! von Jürgen Richard Mankopf Wiesbaden VS Verlag für Sozialwissenschaften 1964 1 Online-Ressource (61 S.) txt rdacontent c rdamedia cr rdacarrier Forschungsberichte des Landes Nordrhein-Westfalen 1307 Probably it is not an exaggeration to say that, since the time of GALILEO who introduced the concept of the harmonic oscillator, we were able to actually ob serve a practically perfect physical image of the latter only when the VAN DER POL oscillator became available relatively a short time ago. In fact, very likely, there exists no better physical image of a simple harmonic motion than that which is produced by modern high quality electron tube oscillators, particulary those whose frequency is stabilized by quartz units. But this almost perfect physical image contains a germ of immense complexity due to the presence of an infinite spectrum of frequencies with which the energy fluctuates between the oscillator and the source of energy. These fluctuations escape our observation, however, if iJ. is very small . . . However, it is precisely this hidden complexity of vanishingly small energy fluctuations which permits obtaining a simple harmonie oscillation in its apparently pure form. N. MINORSKY, Energy Fluctuations 1D a VAN DER POL Oscillator, Journal of the Franklin Intitute 248 (1949). Diese Worte MINORSKYS stellen wir voran, um ein Schlaglicht auf die Bedeutung der v AN DER POLS ehen Differentialgleichung zu werfen. Wir verzichten hier darauf, physikalische und technische Einzelheiten näher auszuführen. Beispiele für V orgänge, die die v AN DER POLsehe Differentialgleichung beschreibt, finden sich in der angegebenen Literatur. Schon die Vielzahl der Vorgänge, die der v AN DER POLS ehen Differentialgleichung gehorchen, rechtfertigt ihr genaues Studium Mathematics Mathematics, general Mathematik https://doi.org/10.1007/978-3-322-98626-9 Verlag Volltext |
| spellingShingle | Mankopf, Jürgen Richard Über die periodischen Lösungen der van der Polschen Differentialgleichung % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qaceWG4bGbamaacqGHRaWkcqaH8oqBdaqadaWdaeaapeGaamiEa8aa % daahaaWcbeqaa8qacaaIYaaaaOGaeyOeI0IaaGymaaGaayjkaiaawM % caaiqadIhagaGaaiabgUcaRiaadIhacqGH9aqpcaaIWaaaaa!43B7! Mathematics Mathematics, general Mathematik |
| title | Über die periodischen Lösungen der van der Polschen Differentialgleichung % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qaceWG4bGbamaacqGHRaWkcqaH8oqBdaqadaWdaeaapeGaamiEa8aa % daahaaWcbeqaa8qacaaIYaaaaOGaeyOeI0IaaGymaaGaayjkaiaawM % caaiqadIhagaGaaiabgUcaRiaadIhacqGH9aqpcaaIWaaaaa!43B7! |
| title_auth | Über die periodischen Lösungen der van der Polschen Differentialgleichung % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qaceWG4bGbamaacqGHRaWkcqaH8oqBdaqadaWdaeaapeGaamiEa8aa % daahaaWcbeqaa8qacaaIYaaaaOGaeyOeI0IaaGymaaGaayjkaiaawM % caaiqadIhagaGaaiabgUcaRiaadIhacqGH9aqpcaaIWaaaaa!43B7! |
| title_exact_search | Über die periodischen Lösungen der van der Polschen Differentialgleichung % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qaceWG4bGbamaacqGHRaWkcqaH8oqBdaqadaWdaeaapeGaamiEa8aa % daahaaWcbeqaa8qacaaIYaaaaOGaeyOeI0IaaGymaaGaayjkaiaawM % caaiqadIhagaGaaiabgUcaRiaadIhacqGH9aqpcaaIWaaaaa!43B7! |
| title_full | Über die periodischen Lösungen der van der Polschen Differentialgleichung % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qaceWG4bGbamaacqGHRaWkcqaH8oqBdaqadaWdaeaapeGaamiEa8aa % daahaaWcbeqaa8qacaaIYaaaaOGaeyOeI0IaaGymaaGaayjkaiaawM % caaiqadIhagaGaaiabgUcaRiaadIhacqGH9aqpcaaIWaaaaa!43B7! von Jürgen Richard Mankopf |
| title_fullStr | Über die periodischen Lösungen der van der Polschen Differentialgleichung % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qaceWG4bGbamaacqGHRaWkcqaH8oqBdaqadaWdaeaapeGaamiEa8aa % daahaaWcbeqaa8qacaaIYaaaaOGaeyOeI0IaaGymaaGaayjkaiaawM % caaiqadIhagaGaaiabgUcaRiaadIhacqGH9aqpcaaIWaaaaa!43B7! von Jürgen Richard Mankopf |
| title_full_unstemmed | Über die periodischen Lösungen der van der Polschen Differentialgleichung % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qaceWG4bGbamaacqGHRaWkcqaH8oqBdaqadaWdaeaapeGaamiEa8aa % daahaaWcbeqaa8qacaaIYaaaaOGaeyOeI0IaaGymaaGaayjkaiaawM % caaiqadIhagaGaaiabgUcaRiaadIhacqGH9aqpcaaIWaaaaa!43B7! von Jürgen Richard Mankopf |
| title_short | Über die periodischen Lösungen der van der Polschen Differentialgleichung % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qaceWG4bGbamaacqGHRaWkcqaH8oqBdaqadaWdaeaapeGaamiEa8aa % daahaaWcbeqaa8qacaaIYaaaaOGaeyOeI0IaaGymaaGaayjkaiaawM % caaiqadIhagaGaaiabgUcaRiaadIhacqGH9aqpcaaIWaaaaa!43B7! |
| title_sort | uber die periodischen losungen der van der polschen differentialgleichung mathtype mtef 2 1 feaagcart1ev2aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9lq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpepekkfr0xfr x fr xb9adbaqaaegacigaaiaabeqaamaabaabaagcbaaeaaaaaaaaa8 qacewg4bgbamaacqghrawkcqah8oqbdaqadawdaeaapegaamiea8aa daahaawcbeqaa8qacaaiyaaaaogaeyoei0iaagymaagaayjkaiaawm caaiqadihagagaaiabgucariaadihacqgh9aqpcaaiwaaaaa 43b7 |
| topic | Mathematics Mathematics, general Mathematik |
| topic_facet | Mathematics Mathematics, general Mathematik |
| url | https://doi.org/10.1007/978-3-322-98626-9 |
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