ISBN: 9781153366786

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 illustra… More...

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. 1890 Excerpt: ...the forces X, Y, Z which act upon a particle, may be such that Xdx + Ydy + Zdz is not an exact differential, so that if the particle were free, there would be no force function, and the equations of motion would not be expressible in the standard form. But if the point move on a surface or a curve, then in the former case Xdx + Ydy + Zdz will be reducible to the form Pdp + Qdq, which will be an exact differential if a single condition (instead of the three conditions which are required in the case of a free particle) be satisfied, and in the latter case it will be reducible to the form Pdp, which is, per se, an exact differential. In the case of a surface, the requisite transformation is given by the Hamiltonian form of the equations of motion, which Jacobi demonstrates for the case in hand; and then in the third section, with a view to its application to the particular case, he enumerates the general proposition quae pro novo principio mechanico haberi potest, which is as follows: Consider the motion of a system of material points subjected to any conditions, and let the forces acting on the several points in the direction of the axes be functions of the coordinates alone: if the determination of the orbits of the several points is reduced to the integration of a single differential equation of the first order between two variables, for this equation there may be found, by a general rule, a multiplier which will render it integrable by quadratures only. And for the particular case the theorem is thus stated: Given three differential equations of the first order between the four quantities?l.?a Pi, Pi, dqt: dq.: dp,: dp2 =::-+ ft:-+0 in which Q Q2 are functions of gu q3 only; suppose that there are known two integrals a,... Arthur Cayley, Books, The Collected Mathematical Papers Of Arthur Cayley Volume 3 Books Volume: 11 Publisher: Cambridge, At the University Press Publication date: 1889 Subjects: Mathematics Mechanics, Analytic Notes: This is an OCR reprint. There may be numerous typos or missing text. There are no illustrations or indexes. When you buy the General Books edition of this book you get free trial access to Million-Books.com where you can select from more than a million books for free. You can also preview the book there.<

ISBN: 1153366789

Taschenbuch, [EAN: 9781153366786], Cambridge Scholars Publishing, Cambridge Scholars Publishing, Book, [PU: Cambridge Scholars Publishing], Cambridge Scholars Publishing, 56214011, Mathem… More...

Taschenbuch, [EAN: 9781153366786], Cambridge Scholars Publishing, Cambridge Scholars Publishing, Book, [PU: Cambridge Scholars Publishing], Cambridge Scholars Publishing, 56214011, Mathematik, 1320308031, Abbildungen, 56248011, Angewandte Mathematik, 1320307031, Forschung, 56263011, Geometrie & Topologie, 56212011, Geschichte, 56227011, Lernen & Lehren, 56217011, Mathematische Analyse, 56272011, Mathematische Physik, 56218011, Matrizen, 56219011, Messung, 56225011, Nachschlagewerke, 56221011, Populär & Elementar, 56230011, Reine Mathematik, 1320309031, Trigonometrie, 56216011, Unendlichkeit, 56220011, Zahlensysteme, 56047011, Fachbücher, 54071011, Genres, 52044011, Fremdsprachige Bücher, 208623031, Taschenbuch, 208621031, Format (binding_browse-bin), 366250011, Refinements, 52044011, Fremdsprachige Bücher<

ISBN: 9781153366786

Volume: 11Publisher: Cambridge, At the University Press Publication date: 1889Subjects: MathematicsMechanics, Analytic Notes: This is an OCR reprint. There may be numerous typos or missin… More...

Volume: 11Publisher: Cambridge, At the University Press Publication date: 1889Subjects: MathematicsMechanics, Analytic Notes: This is an OCR reprint. There may be numerous typos or missing text. There are no illustrations or indexes. When you buy the General Books edition of this book you get free trial access to Million-Books.com where you can select from more than a million books for free. You can also preview the book there. Books, Mathematics~~Essays, The-Collected-Mathematical-Papers-of-Arthur-Cayley~~Arthur-Cayley, 999999999, The Collected Mathematical Papers Of Arthur Cayley (Volume 11), Arthur Cayley, 1153366789, General Books LLC, , , , , General Books LLC<