Edward Routh | |
|---|---|
 Edward John Routh (1831–1907) | |
| Born | Edward John Routh (1831-01-20)20 January 1831[2] Quebec, Canada |
| Died | 7 June 1907(1907-06-07) (aged 76)[2] Cambridge, England |
| Alma mater | University College London Peterhouse, Cambridge |
| Known for | Control theory Routh array Routh polynomials Routh's rule Routh's theorem Routhian mechanics Routh–Hurwitz matrix Routh–Hurwitz stability criterion Routh–Hurwitz theorem |
| Awards | Smith's Prize (1854) Adams Prize (1872) FRS (1872) |
| Scientific career | |
| Fields | Mathematician |
| Institutions | University of London Peterhouse, Cambridge |
| Academic advisors | William Hopkins Augustus De Morgan Isaac Todhunter |
| Notable students | John Strutt (Rayleigh) J. J. Thomson George Darwin Alfred North Whitehead[1] Joseph Larmor |
Edward John RouthFRS (/raʊθ/; 20 January 1831 – 7 June 1907) was an English mathematician, noted as the outstanding coach of students preparing for theMathematical Tripos examination of theUniversity of Cambridge in its heyday in the middle of the nineteenth century.[3] He also did much to systematise the mathematical theory ofmechanics and created several ideas critical to the development of moderncontrol systems theory.
Routh was born of an English father and a French-Canadian mother inQuebec, at that time the British colony ofLower Canada. His father's family could trace its history back to theNorman Conquest when it acquired land atRouth nearBeverley, Yorkshire. His mother's family, the Taschereau family, was well-established in Quebec, tracing their ancestry back to the early days of the French colony. His parents were SirRandolph Isham Routh (1782–1858) and his second wife, Marie Louise Taschereau (1810–1891).[2] Sir Randolph was Commissary General of the British Army 1826, Chairman of the Irish Famine Relief Commission (1845–48) and Deputy Commissary General, the senior Commissariat officer at theBattle of Waterloo, and Marie Louise was the daughter of JudgeJean-Thomas Taschereau and the sister of JudgeJean-Thomas andCardinalElzéar-Alexandre Taschereau.[4]
Routh came to England aged eleven and attendedUniversity College School and then enteredUniversity College, London in 1847, having won a scholarship. There he studied underAugustus De Morgan, whose influence led to Routh to decide on a career in mathematics.[2]
Routh obtained hisBA (1849) andMA (1853) in London.[2] He attendedPeterhouse, Cambridge, where he was taught byIsaac Todhunter and coached by "senior wrangler maker"William Hopkins.[4] While at Peterhouse, Routh rowed forPeterhouse Boat Club.[5] In 1854, Routh graduated just aboveJames Clerk Maxwell, asSenior Wrangler, sharing theSmith's prize with him. Routh was electedfellow of Peterhouse in 1856.[6]
On graduation, Routh took up work as a private mathematics tutor in Cambridge and took on the pupils ofWilliam John Steele during the latter's fatal illness, though insisting that Steele take the fees. Routh inherited Steele's pupils, going on to establish an unbeaten record as a coach. He coached over 600 pupils between 1855 and 1888, 28 of them makingSenior wrangler, as to Hopkins' 17 with 43 of his pupils winningSmith's Prize.[6]
Routh worked conscientiously and systematically, taking rigidly timetabled classes of ten pupils during the day and spending the evenings preparing extra material for the ablest men.[4] "His lectures were enlivened by mathematical jokes of a rather heavy kind."[4]
Routh was a staunch defender of the Cambridge competitive system and despaired when the university started to publish examination results in alphabetical order, observing "They will want to runthe Derby alphabetically next".[4]
Astronomer RoyalGeorge Biddell Airy sought to entice Routh to work at theRoyal Observatory, Greenwich. Though Airy did not succeed, at Greenwich Routh met Airy's eldest daughter Hilda (1840–1916) whom he married in 1864. At the time, the university had a celibacy requirement, forcing Routh to vacate his fellowship and move out of Peterhouse.[7] On the reformation of the college statutes, removing the celibacy requirement, Routh was the first person elected to an honorary fellowship by Peterhouse.[7] The couple had five sons and a daughter. Routh was a "kindly man and a good conversationalist with friends, but with strangers he was shy and reserved."[4]
Routh collaborated withHenry Brougham on theAnalytical View of Sir Isaac Newton's Principia (1855). He published atextbook,Dynamics of a System of Rigid Bodies (1860, 6th ed. 1897) in which he did much to define and systematise the modern mathematical approach tomechanics. This influencedFelix Klein andArnold Sommerfeld. In fact, Klein arranged the German translation.[4] It also did much to influenceWilliam Thomson andPeter Guthrie Tait'sTreatise on Natural Philosophy (1867).[2]
Routh noted the importance of what he called "absent coordinates," also known as cyclic coordinates orignorable coordinates (following the terminology ofE. T. Whittaker in hisAnalytical Dynamics of Particles and Rigid Bodies). Such coordinates are associated with conserved momenta and as such are useful in problem solving.[9] Routh also devised a new method for solving problems in mechanics. AlthoughRouth's procedure does not add any new insights, it allows for more systematic and convenient analysis, especially in problems with many degrees of freedom and at least some cyclic coordinates.[10][11]
In addition to his intensive work in teaching and writing, which had a persistent effect on the presentation ofmathematical physics, he also contributed original research such as theRouth–Hurwitz theorem.
Central tenets of moderncontrol systems theory relied upon theRouth stability criterion (though nowadays due to modern computers it is not as important), an application ofSturm's theorem to evaluateCauchy indices through the use of theEuclidean algorithm.
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