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Energie cinetică

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Definiţie Edit

Teorema energiei cinetice pentru un sistem de puncte materiale Edit

\sum_i m_i  \frac{d \vec v_i}{dt} d \vec r_i = \sum_i \vec R_i \cdot d \vec r_i + \sum_i \sum_j \vec F_{ij} \cdot d \vec r_i \!
d L_{int} = \sum_i \sum_j \vec F_{ij} \cdot d \vec r_i  \! - lucrul mecanic elementar al forţelor interioare
d L_{ext} = \sum_i \vec R_i \cdot d \vec r_i \! - lucrul mecanic elementar al forţelor exterioare
\sum_i m_i  \frac{d \vec v_i}{dt} d \vec r_i  = \sum_i m_i \frac{d \vec v_i}{dt} (\vec v_i dt) = d \left [ \sum_i \frac  12 m_i v_i^2 \right ] \!
d \left [ \sum_i \frac  12 m_i v_i^2 \right ] = d L_{ext} + d L_{int} \!
T = \sum_i \frac 1 2 m_i v_i^2 \!
dT = d L_{ext}+ d L_{int} \!
dT = 0 \; \Rightarrow \; T=const. \!

Vezi şi Edit

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