Given the single degree of freedom (SDOF) equation of motion mv\'\'(t) + cv\'(t)
ID: 1710228 • Letter: G
Question
Given the single degree of freedom (SDOF) equation of motion mv''(t) + cv'(t) + kv(t) = p(t). This basic equation of motion in structural dynamics is concerned with the displacement, velocity (first-order derivative with respect to displacement) and acceleration (second-order derivative with respect to displacement) of the structure. Why do we stop at acceleration (the second-order derivative), and ignore higher-order derivatives with respect to displacement in the equation of motion. Please include all sources (e.g. reference) you have used.
Bonus Question (3 Points): Given the single degree of freedom (SDoF) equation of motion This basic equation of motion in structural dynamics is concerned with the displacement, velocity (first-order derivative with respect to displacement and acceleration (second-order derivative with respect to displacement of the structure. Why do we stop at acceleration (the second-order derivative), and ignore higher-order derivatives with respect to displacement in the equation of motion. [Open question, please include all sources (e.g. reference) you have used]Explanation / Answer
As the equations of motion are of second order, the higher derivatives does not give any new information (but follow uniquely from the initial conditions of position and velocity), therefore they usually are not discussed.
As Timaeus pointed out there are specific scenarios, e.g. Norton's dome where intial values for the higher order derivates will change the outcome, this has to do with singular solutions of ODE, but these are unstable against infinitesimal perturbations, so we would not consider them usually.
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