“linearization”的概念、定义、习题解题方法及翻译-数学辞典

单词

linearization

释义

linearization

For a small quantity x, higher order terms x2, x3,… are yet smaller by comparison. Linearization considers such higher-order terms negligible, so as to simplify an equation with the aim of finding an approximate solution. For example, a simple pendulum that makes the angle θ with the downward vertical satisfies

where $inline$ denotes acceleration due to gravity and $inline$ is the length of the pendulum. The solutions involve elliptic integrals. However, for small oscillations θ about the vertical, a linear approximation of sinθ is θ, which gives the equation for simple harmonic motion, and so the exact solution can instead be approximated with trigonometric functions. See linear theory of equilibria.

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