An Elementary Treatise On the Dynamics of a System of Rigid Bodies. With Numerous Examples
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12 &c. = &c.
Also since T is a homogeneous function of the second order in ql,q^..-t[n w^e have dT dT Hence the equation of vis viva may be written in the form 2(^+;.)=^2/-Hf^;-i- (D).
ON THE GENERAL EQUATIONS OP MOTION. i251 The quantities g',', q^...qj maybe eliminated from the equations (A') and (D), and we have a partial differential equation, which may be written in the form of a determinant, to find F.
Also if we consider the initial value of T, we shall have another equation of a similar... form with a^,a^. . .a„ written instead of q^, q^. . .q^. It is necessary that the function F should satisfy both these equations.
If we wrote PitP^--- for -j— , -j— . . . this process of finding q,'qj... from the equations (A') and substituting in the equa- tion of vis viva exactly corresponds to the Hamiltonian pro- cess of expressing Zf= T— U in terms of p^,p^...qi,q^...H then we write the Hamiltonian function H in the form the differential equation to find V will be 173. By the preceding reasoning all the integrals of a dynamical system of equations can be expressed in terms of the differential coeflScients of a single function V.
What to read after An Elementary Treatise On the Dynamics of a System of Rigid Bodies. With Numerous Examples?
You can find similar books in the "Read Also" column, or choose other free books by Edward John Routh to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
12 &c. = &c.
Also since T is a homogeneous function of the second order in ql,q^..-t[n w^e have dT dT Hence the equation of vis viva may be written in the form 2(^+;.)=^2/-Hf^;-i- (D).
ON THE GENERAL EQUATIONS OP MOTION. i251 The quantities g',', q^...qj maybe eliminated from the equations (A') and (D), and we have a partial differential equation, which may be written in the form of a determinant, to find F.
Also if we consider the initial value of T, we shall have another equation of a similar... form with a^,a^. . .a„ written instead of q^, q^. . .q^. It is necessary that the function F should satisfy both these equations.
If we wrote PitP^--- for -j— , -j— . . . this process of finding q,'qj... from the equations (A') and substituting in the equa- tion of vis viva exactly corresponds to the Hamiltonian pro- cess of expressing Zf= T— U in terms of p^,p^...qi,q^...H then we write the Hamiltonian function H in the form the differential equation to find V will be 173. By the preceding reasoning all the integrals of a dynamical system of equations can be expressed in terms of the differential coeflScients of a single function V.
What to read after An Elementary Treatise On the Dynamics of a System of Rigid Bodies. With Numerous Examples?
You can find similar books in the "Read Also" column, or choose other free books by Edward John Routh to read onlineMoreLess
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