ヒル微分方程式

数学におけるヒル微分方程式(ヒルびぶんほうていしき、: Hill differential equation)あるいはヒル方程式(ヒルほうていしき、: Hill equation)とは、次の形状の二階線型常微分方程式のことを言う。

ここで f(t)周期函数である[1]。1886年にこの方程式を発見した、ジョージ・ウィリアム・ヒルの名にちなむ[2]

f(t) の周期は 2π であると仮定することも出来る。このときヒル微分方程式は、f(t) のフーリエ級数を用いて次のように表すことが出来る。

ヒル微分方程式の特別な場合として重要なものには、マシュー方程式n = 0, 1 に対応する項のみが含まれている場合)やマイスナー方程式などがある。

ヒル微分方程式は、周期微分方程式の理解に役立つ重要な例の一つである。f(t) の正確な形状に依存して、ヒル微分方程式の解はすべての時間に対して有界な領域にとどまるか、あるいはその振動の振幅が指数関数的に成長を続けるかのいずれかである[3]。ヒル微分方程式の解の正確な形は、フロケ理論によって表現される。その解はまた、ヒル行列式の観点からも表現される。

ヒル微分方程式は、もともとは月の安定性への応用が考えられていたが、その他にも四重極質量分析計英語版のモデリングや、加速器科学英語版においてなど、多くの応用が考えられるものである。四重極質量分析計は、水晶内での電子に関する一次元シュレディンガー方程式としてモデル化される。

参考文献

  1. ^ Magnus, W.; Winkler, S. (1966). Hill's equation. New York-London-Sydney: Interscience Publishers John Wiley & Sons 
  2. ^ Hill, G.W. (1886). “On the part of the motion of lunar perigee which is a function of the mean motions of the sun and moon”. Acta Math. 8 (1): 1–36. doi:10.1007/BF02417081. 
  3. ^ Teschl, Gerald (2012). Ordinary Differential Equations and Dynamical Systems. Providence: American Mathematical Society. ISBN 978-0-8218-8328-0. http://www.mat.univie.ac.at/~gerald/ftp/book-ode/ 

外部リンク

Read other articles:

IFAR 22 Jenis Senapan serbu bullpup Negara asal Indonesia Sejarah pemakaian Digunakan oleh Lihat Pengguna Sejarah produksi Perancang PT Republik Armamen Industri Produsen PT Republik Armamen Industri Spesifikasi Berat 3.6 kg (menggunakan laras 16 inci)3.7 kg (menggunakan laras 20 inci) Panjang 698 mm (menggunakan laras 16 inci)780 mm (menggunakan laras 20 inci) Kaliber 5,56 × 45 mm NATO Mekanisme Pengisian peluru dengan gas Rata² tembakan 600–800 rpm Jarak efektif 400...

 

Не следует путать с Верховная распорядительная комиссия.Отделение по охранению общественной безопасности и порядкарус. дореф. Отдѣленіе по охраненію общественной безопасности и порядка Страна  Российская империя Создана 1866 Распущена (преобразована) 4 марта 1917 года �...

 

Brighton & Hove AlbionNama lengkapBrighton & Hove Albion Football ClubJulukanThe SeagullsThe AlbionBerdiri24 Juni 1901; 122 tahun lalu (1901-06-24)StadionStadion Falmer[1](Kapasitas: 30.750[2])Ketua Tony BloomPelatih Kepala Roberto De ZerbiLigaLiga Utama Inggris2022–2023ke-6, Liga Utama InggrisSitus webSitus web resmi klub Kostum kandang Kostum tandang Kostum ketiga Musim ini Brighton & Hove Albion Football Club adalah sebuah klub sepak bola profesional...

BBC Radio 2Logo sejak 2022KotaLondon dan ManchesterWilayah siarBritania Raya dan International via Satelit dan BBC SoundsMulai mengudara30 September 1967; 56 tahun lalu (1967-09-30)FormatAdult contemporary musicVarious specialist musik programBahasaInggrisKode panggil sebelumnyaBBC Light ProgrammeFrekuensi sebelumnya200 kHz (1967–1978)909 kHz (1978–1990)PemilikBBCStasiun kembarBBC Radio 6 MusicSiaran webBBC SoundsSitus webwww.bbc.co.uk/radio2 BBC Radio 2 adalah stasiun radio nasional...

 

Bosnian middle-distance runner Abedin MujezinovićMujezinović at Munich 2022Personal informationNationalityBosnianBorn (1993-06-02) 2 June 1993 (age 30)Zenica, Republic of Bosnia and Herzegovina[1]SportCountry Bosnia and HerzegovinaSportTrack and fieldEvent800 metresClubAK SarajevoCoached byGianni GhidiniAchievements and titlesHighest world ranking55Personal best(s)400 m: 47.58 (2019) 800 m: 1:45.32 (2023) Medal record Men's athletics Representing  Bosnia and Herzegovi...

 

Curiosity museum located in Loveland, Ohio USA For other uses, see Château de la Roche (disambiguation). Château LarocheChâteau Laroche, The Loveland CastleEstablished1929LocationSymmes Township, Hamilton County, Ohio, USCoordinates39°17′00″N 84°15′58″W / 39.283234°N 84.266225°W / 39.283234; -84.266225TypeCuriosity museumDirectorMaintained by the KOGTWebsitewww.lovelandcastle.com Château Laroche, also known as the Loveland Castle, is a museum on the ban...

† Человек прямоходящий Научная классификация Домен:ЭукариотыЦарство:ЖивотныеПодцарство:ЭуметазоиБез ранга:Двусторонне-симметричныеБез ранга:ВторичноротыеТип:ХордовыеПодтип:ПозвоночныеИнфратип:ЧелюстноротыеНадкласс:ЧетвероногиеКлада:АмниотыКлада:Синапсиды�...

 

Title given to a messenger or receiver of knowledge, especially in Christianity Not to be confused with apostille (international legal document) or apostil (commentary in margins). For other uses, see Apostolos. For the primary historical disciples of Jesus, see Apostles in the New Testament. For other uses, see Apostle (disambiguation). Some of the Twelve Apostles. Mosaic in the Euphrasian Basilica. An apostle (/əˈpɒsəl/), in its literal sense, is an emissary. The word is derived from An...

 

artikel ini perlu dirapikan agar memenuhi standar Wikipedia. Tidak ada alasan yang diberikan. Silakan kembangkan artikel ini semampu Anda. Merapikan artikel dapat dilakukan dengan wikifikasi atau membagi artikel ke paragraf-paragraf. Jika sudah dirapikan, silakan hapus templat ini. (Pelajari cara dan kapan saatnya untuk menghapus pesan templat ini) BlackRockIndustrijasa investasiDidirikan1988KantorpusatAmerika SerikatWilayah operasiSeluruh duniaPendapatan US$ 10.5 milyar (2013)[1]Laba...

Bangladeshi cricketer For the train driver, see Salma Khatun (train driver). Salma KhatunKhatun in 2018Personal informationBorn (1990-10-01) 1 October 1990 (age 33)Khulna, BangladeshHeight5 ft 5 in (1.65 m)BattingRight-handedBowlingRight-arm off breakRoleAll-rounderInternational information National sideBangladesh (2011–present)ODI debut (cap 7)26 November 2011 v IrelandLast ODI17 December 2022 v New ZealandT20I debut (cap 8)28 Augus...

 

Da Hustler redirects here. Not to be confused with The Hustler. 1999 studio album by NoreagaMelvin Flynt - Da HustlerStudio album by NoreagaReleasedAugust 24, 1999 (1999-08-24)Recorded1998-99StudioThe Hit Factory (New York, NY)Sound On Sound (New York, NY)Criteria Studios (Miami, FL)GenreGangsta rapLength1:10:23LabelPenaltyProducerAnthony BarnersCharly Suga Bear CharlesEZ ElpeeJamal EdgertonMannie FreshSPKillaSwizz BeatzThe NeptunesTrackmastersNoreaga chronology N.O.R.E...

 

City in Washington, United StatesSequim, WashingtonCityJohn Wayne Marina in SequimSequim, WashingtonCoordinates: 48°4′41″N 123°6′5″W / 48.07806°N 123.10139°W / 48.07806; -123.10139CountryUnited StatesStateWashingtonCountyClallamGovernment • TypeCouncil–manager[1] • MayorTom Ferrell[2]Area[3] • Total6.40 sq mi (16.58 km2) • Land6.32 sq mi (16.37 km2) ...

Disambiguazione – Se stai cercando altri significati, vedi Epifania (disambigua). Questa voce o sezione sull'argomento Cristianesimo non è ancora formattata secondo gli standard. Commento: Tutte le note usano il template inglese quando presente Contribuisci a migliorarla secondo le convenzioni di Wikipedia. Segui i suggerimenti del progetto di riferimento. Epifania del SignoreParticolare dell'Adorazione dei Magi di Gentile da Fabriano, Galleria degli Uffizi.Tiporeligiosa Data6 ge...

 

هذه المقالة يتيمة إذ تصل إليها مقالات أخرى قليلة جدًا. فضلًا، ساعد بإضافة وصلة إليها في مقالات متعلقة بها. (أغسطس 2022) جارديل معلومات شخصية الميلاد 10 أكتوبر 1989 (35 سنة)  بلوميناو  الطول 1.93 م (6 قدم 4 بوصة) مركز اللعب مهاجم الجنسية البرازيل  معلومات النادي النادي ال...

 

Bowel dysfunction Medical conditionConstipationOther namesCostiveness,[1] dyschezia[2]Constipation in a young child seen on X-ray. Circles represent areas of fecal matter (stool is white surrounded by black bowel gas).SpecialtyGastroenterologySymptomsInfrequent or hard to pass bowel movements, abdominal pain, bloating[2][3]ComplicationsHemorrhoids, anal fissure, fecal impaction[4]CausesSlow movement of stool within the colon, irritable bowel syndrome, c...

German mathematician (1815–1897) Karl WeierstrassKarl WeierstraßBorn(1815-10-31)31 October 1815Ennigerloh, Province of Westphalia, Kingdom of PrussiaDied19 February 1897(1897-02-19) (aged 81)Berlin, Kingdom of Prussia, German EmpireNationalityGermanAlma materUniversity of BonnMünster AcademyKnown forWeierstrass functionWeierstrass product inequality(ε, δ)-definition of limitWeierstrass–Erdmann conditionWeierstrass theoremsBolzano–Weierstrass theoremAwardsPhD (Hon): Un...

 

Probability of an event occurring, given that another event has already occurred Part of a series on statisticsProbability theory Probability Axioms Determinism System Indeterminism Randomness Probability space Sample space Event Collectively exhaustive events Elementary event Mutual exclusivity Outcome Singleton Experiment Bernoulli trial Probability distribution Bernoulli distribution Binomial distribution Exponential distribution Normal distribution Pareto distribution Poisson distribution...

 

Night Fighters redirects here. For the 1960 film also known as The Night Fighters, see A Terrible Beauty (film). Fighter aircraft adapted or designed for use at night Night fighter / All-weather fighterTop left: Swedish de Havilland Venom NF.51 (J 33), during night operation 1954Top right: The nose of a German Lichtenstein radar-equipped Messerschmitt Bf 110 G-4 night fighterBottom left: American Northrop P-61 Black Widow night fighter with a radome nose for its radarBottom right: A de Havill...

معركة بروزة جزء من الحرب العثمانية - البندقية (1537 - 1540) خير الدين بربروس يهزم العصبة المقدسة (1538م) بقيادة أندريا دوريا في معركة بروزة معلومات عامة التاريخ 28 سبتمبر 1538 الموقع بريفيزا (البحر الأيوني)38°57′33″N 20°45′01″E / 38.9592°N 20.7503°E / 38.9592; 20.7503   النتيجة نصر حاسم للع...

 

Research of materials This article includes a list of general references, but it lacks sufficient corresponding inline citations. Please help to improve this article by introducing more precise citations. (August 2023) (Learn how and when to remove this message) A diamond cuboctahedron showing seven crystallographic planes, imaged with scanning electron microscopy Six classes of conventional engineering materials Materials science is an interdisciplinary field of researching and discovering m...