The Advanced Part of a Treatise On the Dynamics of a System of Rigid Bodies: Being Part Ii. of a Treatise On the Whole Subject. with Numerous Examples, Part 2

Routh, Edward John

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Title: The Advanced Part of a Treatise On the ...
Publisher: Ulan Press


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Edward John Routh
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Book Description Palala Press, United States, 2016. Hardback. Book Condition: New. 234 x 156 mm. Language: N/A. Brand New Book ***** Print on Demand *****. Bookseller Inventory # APC9781357580902

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Edward John Routh
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Book Description Palala Press, United States, 2016. Hardback. Book Condition: New. 234 x 156 mm. Language: N/A. Brand New Book ***** Print on Demand *****. Bookseller Inventory # APC9781357580902

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Edward John Routh
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Book Description Not Avail, United States, 2012. Paperback. Book Condition: New. 246 x 189 mm. Language: English . Brand New Book ***** Print on Demand *****. This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1892 Excerpt: .free vibrations in the expression for y, viz. = n and two equal values of X each zero. These equal values introduce the terms with powers of t as explained in Art. 266. We infer that any small permanent periodical force produces a magnified disturbance both in the radius vector and longitude of a planet, if its period is nearly equal to that of the planet or is very long. Since there are two equal free periods in the longitude whose type is X = 0 and only one in the radius vector, those small disturbing forces whose periods are very long are twice magnified in their effects on the longitude and once magnified in the radius vector. If any such forces as these act on the planet it is necessary to examine into their effects. Small disturbing forces, whose magnitudes are less than the standard of small quantities to be retained, may be disregarded only if their periods are different from those just indicated. These rules are used in the Lunar and Planetary Theories to assist us in estimating the values of the disturbing forces. They enable us to separate from the crowd of small forces those which can produce sensible effects on the motions of the planets, see Art. 337. 346. How a disturbing force is diminished. Let us resume the expression given in Art. 326 for the forced vibration due to a continuous disturbing force. We remark in the first place that the denominator of the coefficient contains higher powers of than the numerator. To show this it may be sufficient to notice that the determinant of the motion A (8) has two powers of 8 more than any of its minors. We therefore infer that, in the limit, when is very great, i.e. when the period of the disturbing force is much smaller than that of any free oscillation, the forced vibration produced is in general in. Bookseller Inventory # APC9781236377913

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ISBN 10: 1236196082 ISBN 13: 9781236196088
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Book Description Rarebooksclub.com, United States, 2012. Paperback. Book Condition: New. 246 x 189 mm. Language: English . Brand New Book ***** Print on Demand *****. This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1892 Excerpt: .On the wire a small weight slides by means of which it may be made to vibrate in the same time as the pendulum to which it is to be applied as a test. When thus adjusted it is placed on the material to which the pendulum is attached, and should this not be perfectly firm, the motion will be communicated to the wire, which in a little time will accompany the pendulum on its vibrations. This ingenious contrivance appeared fully adequate to the purpose for which it was employed, and afforded a satisfactory proof of the stability of the point of suspension. See Phil. Trans. 1818. 343. It has been shown in Art. 338 that a disturbing force may produce a large vibration in x if its period is such that the denominator A (J) is small. But this result is affected by the operator / (5) which occurs in the numerator. If for instance the result of the operation of the minor I ($) is zero, the forced vibration disappears. Now these minors are just the operators used in finding the free vibrations. Thus in Art. 262, we have x = I(S) type. If then any one of the free vibrations is absent from one of the co-ordinates though present in the others, then a disturbing force of nearly the same period does not produce a large forced vibration in that co-ordinate. We infer that a disturbing force can produce a large forced vibration in any co-ordinate only if there be in tha t co-ordinate a free vibration of nearly the same period and containing nearly the same real exponential. 344. If the force is nearly equal to Pe sin (XJ + a), it may occur that the determinant A (5) has a roots equal to-K + j-1, while the minor I (5) has none of them. Referring to the expressions for the forced vibrations in the co-ordinates x, y, o. given in Art. 326, we see that in this case the forced. Bookseller Inventory # APC9781236196088

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Book Description RareBooksClub. Paperback. Book Condition: New. This item is printed on demand. Paperback. 182 pages. Dimensions: 9.7in. x 7.4in. x 0.4in.This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1892 Excerpt: . . . On the wire a small weight slides by means of which it may be made to vibrate in the same time as the pendulum to which it is to be applied as a test. When thus adjusted it is placed on the material to which the pendulum is attached, and should this not be perfectly firm, the motion will be communicated to the wire, which in a little time will accompany the pendulum on its vibrations. This ingenious contrivance appeared fully adequate to the purpose for which it was employed, and afforded a satisfactory proof of the stability of the point of suspension. See Phil. Trans. 1818. 343. It has been shown in Art. 338 that a disturbing force may produce a large vibration in x if its period is such that the denominator A (J) is small. But this result is affected by the operator (5) which occurs in the numerator. If for instance the result of the operation of the minor I () is zero, the forced vibration disappears. Now these minors are just the operators used in finding the free vibrations. Thus in Art. 262, we have x I(S) type. If then any one of the free vibrations is absent from one of the co-ordinates though present in the others, then a disturbing force of nearly the same period does not produce a large forced vibration in that co-ordinate. We infer that a disturbing force can produce a large forced vibration in any co-ordinate only if there be in tha t co-ordinate a free vibration of nearly the same period and containing nearly the same real exponential. 344. If the force is nearly equal to Pe sin (XJ a), it may occur that the determinant A (5) has a roots equal to-K j-1, while the minor I (5) has none of them. Referring to the expressions for the forced vibrations in the co-ordinates x, y, and o. given in Art. 326, we see that in this case the forced. . . This item ships from La Vergne,TN. Paperback. Bookseller Inventory # 9781236196088

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Book Description Not Avail, United States, 2012. Paperback. Book Condition: New. 246 x 189 mm. Language: English . Brand New Book ***** Print on Demand *****.This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1892 Excerpt: .free vibrations in the expression for y, viz. = n and two equal values of X each zero. These equal values introduce the terms with powers of t as explained in Art. 266. We infer that any small permanent periodical force produces a magnified disturbance both in the radius vector and longitude of a planet, if its period is nearly equal to that of the planet or is very long. Since there are two equal free periods in the longitude whose type is X = 0 and only one in the radius vector, those small disturbing forces whose periods are very long are twice magnified in their effects on the longitude and once magnified in the radius vector. If any such forces as these act on the planet it is necessary to examine into their effects. Small disturbing forces, whose magnitudes are less than the standard of small quantities to be retained, may be disregarded only if their periods are different from those just indicated. These rules are used in the Lunar and Planetary Theories to assist us in estimating the values of the disturbing forces. They enable us to separate from the crowd of small forces those which can produce sensible effects on the motions of the planets, see Art. 337. 346. How a disturbing force is diminished. Let us resume the expression given in Art. 326 for the forced vibration due to a continuous disturbing force. We remark in the first place that the denominator of the coefficient contains higher powers of than the numerator. To show this it may be sufficient to notice that the determinant of the motion A (8) has two powers of 8 more than any of its minors. We therefore infer that, in the limit, when is very great, i.e. when the period of the disturbing force is much smaller than that of any free oscillation, the forced vibration produced is in general in. Bookseller Inventory # APC9781236377913

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Book Description Book on Demand, Miami, 2016. Perfect binding. Book Condition: NEW. Dust Jacket Condition: NEW. 5.8" x 8.3". In English language. This book, "The Advanced Part of a Treatise On the Dynamics of a System of Rigid Bodies: Being Part Ii. of a Treatise On the Whole Subject. with Numerous Examples, Part 2", by Edward John Routh, is a replication. It has been restored by human beings, page by page, so that you may enjoy it in a form as close to the original as possible. This item is printed on demand. Thank you for supporting classic literature. SOFT COVER. Bookseller Inventory # 1557245

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Book Description Rarebooksclub.com, United States, 2012. Paperback. Book Condition: New. 246 x 189 mm. Language: English . Brand New Book ***** Print on Demand *****.This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1892 Excerpt: .On the wire a small weight slides by means of which it may be made to vibrate in the same time as the pendulum to which it is to be applied as a test. When thus adjusted it is placed on the material to which the pendulum is attached, and should this not be perfectly firm, the motion will be communicated to the wire, which in a little time will accompany the pendulum on its vibrations. This ingenious contrivance appeared fully adequate to the purpose for which it was employed, and afforded a satisfactory proof of the stability of the point of suspension. See Phil. Trans. 1818. 343. It has been shown in Art. 338 that a disturbing force may produce a large vibration in x if its period is such that the denominator A (J) is small. But this result is affected by the operator / (5) which occurs in the numerator. If for instance the result of the operation of the minor I ($) is zero, the forced vibration disappears. Now these minors are just the operators used in finding the free vibrations. Thus in Art. 262, we have x = I(S) type. If then any one of the free vibrations is absent from one of the co-ordinates though present in the others, then a disturbing force of nearly the same period does not produce a large forced vibration in that co-ordinate. We infer that a disturbing force can produce a large forced vibration in any co-ordinate only if there be in tha t co-ordinate a free vibration of nearly the same period and containing nearly the same real exponential. 344. If the force is nearly equal to Pe sin (XJ + a), it may occur that the determinant A (5) has a roots equal to-K + j-1, while the minor I (5) has none of them. Referring to the expressions for the forced vibrations in the co-ordinates x, y, o. given in Art. 326, we see that in this case the forced. Bookseller Inventory # APC9781236196088

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