Elements of Analytical Mechanics
Elements of Analytical Mechanics
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§ 130. — Regarding the forces as applied directly to the centre of inertia, replace in Equations (117), the values 2 P. Cos a, 2 P. Cos /3, and 2 P . Cos y, by X, Y, and Z, respectively, and we may write, Y-M -^-0 (120) from which the accents are omitted, and in which a*, y, and z, must be understood as appertaining to the centre of inertia.
GEJSTEEAL THEOEEM OF WOEK, VELOCITY AND LIVING FOECE.
§131. — Multiply the first of Equations (120) by 2dx, the second by 2dy, the third by 2dz, add and in...tegrate, we have 2f{Xdx + Ydy + Zdz) - M. '^'^' "*" ^^^ ^ ^^^ + C = 0, But whence, dt^ dx^ + r Z, y2 -f- dz''" _ d^ _ ^ dfi ~ dfi ~ ' 2f{Xdx + Ydy + Zdz) - If. V^+ C = (121) The first term is, § 101, twice the quantity of Avork of the ex- traneous forces, the second is twice the quantity of work of the inertia, measured by the living force, and the third is the constant of integration.
If the forces X, Y, Z, be variable, they must be expressed in functions of x, y, s, before the integration can be performed.
What to read after Elements of Analytical Mechanics?
You can find similar books in the "Read Also" column, or choose other free books by W H C William Holms Chambers Bartlett to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
§ 130. — Regarding the forces as applied directly to the centre of inertia, replace in Equations (117), the values 2 P. Cos a, 2 P. Cos /3, and 2 P . Cos y, by X, Y, and Z, respectively, and we may write, Y-M -^-0 (120) from which the accents are omitted, and in which a*, y, and z, must be understood as appertaining to the centre of inertia.
GEJSTEEAL THEOEEM OF WOEK, VELOCITY AND LIVING FOECE.
§131. — Multiply the first of Equations (120) by 2dx, the second by 2dy, the third by 2dz, add and in...tegrate, we have 2f{Xdx + Ydy + Zdz) - M. '^'^' "*" ^^^ ^ ^^^ + C = 0, But whence, dt^ dx^ + r Z, y2 -f- dz''" _ d^ _ ^ dfi ~ dfi ~ ' 2f{Xdx + Ydy + Zdz) - If. V^+ C = (121) The first term is, § 101, twice the quantity of Avork of the ex- traneous forces, the second is twice the quantity of work of the inertia, measured by the living force, and the third is the constant of integration.
If the forces X, Y, Z, be variable, they must be expressed in functions of x, y, s, before the integration can be performed.
What to read after Elements of Analytical Mechanics?
You can find similar books in the "Read Also" column, or choose other free books by W H C William Holms Chambers Bartlett to read onlineMoreLess
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