06.09.2021 Views

Direct Energy, 2018a

Direct Energy, 2018a

Direct Energy, 2018a

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

12 RELATING ENERGY CONVERSION PROCESSES 277<br />

<strong>Energy</strong><br />

storage<br />

device<br />

Generalized<br />

Path<br />

Generalized<br />

Potential<br />

Generalized<br />

Capacity<br />

Constitutive<br />

relationship<br />

<strong>Energy</strong><br />

Law for<br />

potential<br />

Linear<br />

Spring<br />

−→ F Force in<br />

J<br />

m = N<br />

Displacement<br />

−→ x in m<br />

K in J m 2 1<br />

K<br />

Linear<br />

Spring<br />

Displacement<br />

−→ x in m<br />

−→ F Force in<br />

J<br />

m = N<br />

in<br />

m2<br />

J<br />

−→ F = K<br />

−→ x<br />

−→ x =<br />

1<br />

−→<br />

K F<br />

Newton's<br />

Second Law<br />

−→ F = m<br />

−→ a<br />

Flywheel<br />

−−→ ωang<br />

Angular<br />

Velocity in<br />

rad<br />

s<br />

−−→<br />

Lam<br />

Angular<br />

Momentum<br />

in J·s<br />

Flywheel<br />

−−→<br />

Lam<br />

Angular<br />

Momentum<br />

in J·s<br />

−−→<br />

ω ang<br />

Angular<br />

Velocity in<br />

rad<br />

s<br />

1<br />

I in 1<br />

I in kg · m<br />

kg·m 2<br />

2<br />

−−→<br />

−−→<br />

ωang =<br />

1L I am<br />

1<br />

K|−→ x | 2 1<br />

= I |−−→ ω<br />

2 2 ang | 2 =<br />

1 1<br />

|−→ F | 2 2 K ∣L −−→ ∣ ∣∣<br />

2<br />

am<br />

Newton's<br />

Second Law<br />

−→ F = m<br />

−→ a<br />

1 1<br />

2 I<br />

Conservation<br />

of Angular<br />

Momentum<br />

−−→<br />

Lam =<br />

I −−→ ω ang<br />

Conservation<br />

of Angular<br />

Momentum<br />

Table 12.4: Describing mechanical systems in the language of calculus of<br />

variations.

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!