An Elementary Treatise On the Dynamics of a System of Rigid Bodies
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432. Also let F{D} be the minor of the leading con- stituent ; the value of x is then known to be ^ = l^Qei^i + M^e'^^*+ The term Qe^ in the differential equation is the analytical representation of some small periodical force which acts on the system. The first term of the expression for x is the direct effect of the force, and is sometimes called the ■forced vibration in the co-ordinate x. The quantities m^, m^, &c. being generally imaginary, the remaining terms are also trigonometrical and a...re sometimes called the free or natural vibrations in the co-ordinate. In the analytical theory of linear differential equations, the forced vibration is called the particular integral and the free vibration the complementary function.
498. If we examine the coefficient of the forced vibration in x we shall see that it is large only if /(/*) is very small or zero. Since the roots of the equation f(fji.) = are m^, m^, &c. the rule may be simply stated thus : amj small periodical term whose coefficient in the differential equation is less than the standard of quantities to be neglected may rise into importance if its period is nearly equal to one of the free vibrations of the system.
What to read after An Elementary Treatise On the Dynamics of a System of Rigid Bodies?
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:
432. Also let F{D} be the minor of the leading con- stituent ; the value of x is then known to be ^ = l^Qei^i + M^e'^^*+ The term Qe^ in the differential equation is the analytical representation of some small periodical force which acts on the system. The first term of the expression for x is the direct effect of the force, and is sometimes called the ■forced vibration in the co-ordinate x. The quantities m^, m^, &c. being generally imaginary, the remaining terms are also trigonometrical and a...re sometimes called the free or natural vibrations in the co-ordinate. In the analytical theory of linear differential equations, the forced vibration is called the particular integral and the free vibration the complementary function.
498. If we examine the coefficient of the forced vibration in x we shall see that it is large only if /(/*) is very small or zero. Since the roots of the equation f(fji.) = are m^, m^, &c. the rule may be simply stated thus : amj small periodical term whose coefficient in the differential equation is less than the standard of quantities to be neglected may rise into importance if its period is nearly equal to one of the free vibrations of the system.
What to read after An Elementary Treatise On the Dynamics of a System of Rigid Bodies?
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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