• Keine Ergebnisse gefunden

106 GHAPTER

N/A
N/A
Info
Herunterladen
Protected

Academic year: 2022

Aktie "106 GHAPTER "

Copied!
1
0
0

Wird geladen.... (Jetzt Volltext ansehen)

Jetzt herunterladen ( 1 Seite )

Volltext

(1)

106 GHAPTER

4

SEGOND-ORDER THEORY

OF

EQUILIBRIUM FIGURES

x

'TTteridian of surface

of revolution ---

---

...

x

0

y

r

()

R

2

~---~~---~-y

surjace no1'1'71al Q

I

,

\

\

\ '\ '\

"-...

---

FIGURE 4.7: The normal radius of curvature

"- '\

'\

\

. /

/ / /

\

\

,

I I I / /

order to have :z: = r cos 0, y = r sin 0 as usual for plane polar coordinates). This holds not only for the ellipsoid, but also for an arbitrary surface of revolution; cf. sec. 1.4.

From Fig. 4.7 we read

y

=

r sin 0

=

R2 sin 0' whence

(4-150)

The elementary tri angle at P, shown in a magnified manner next to the main diagram (Fig. 4.7), gives

. 0' d:z:

Sin =---

ds (4-151)

Differentiating :z:

=

r cos 0 we have

d:z: = dr cos () - r sin OdO (4-152)

Furthermore,

(4-153) In both formulas we put

dr = redO (4-154)

by (4-149); in fact, by (4-147), r depends on 0 only, so that here 8r dr

re = 80 = dO (4-155)

~h

Referenzen

Jetzt herunterladen ( PDF - 1 Seite - 168.81 KB )

ÄHNLICHE DOKUMENTE

To approve or not to approve: this is not the only question

2 In particular we do not allow that all voters cast abstain/negative votes for all candidates. With this requirement we avoid stating that all candidates must be elected in case

The Next (but not new) Frontier for Sovereign Default

First, domestic debt is and was large—for the 64 countries for which we have long time series, domestic debt averages almost two-thirds of total public debt; the increase in the

Evolution, not revolution, for Japan’s military posture

The overall impact of these changes will not, however, result in a change in Japanese regional strategic goals and will only result in incremental changes to Japan’s military

not the only person

Peetre, Rectification ` a l’article “Une caract´ erisation abstraite des op´ erateurs diff´ erentiels” Math.. Friedrichs, On the differentiability of the solutions of linear

σ holds for

With topos we mean Grothendieck topos, and as metatheory we use a con- structive but impredicative flavour of English (which could be formalised by what is supported by the

q To do this credibly, we have had to hide not only the existence of the details but also the performance conse uences of hiding them

The most important example is the synergy between the register allocation and the instruction scheduler he scheduler tends to do much better at scheduling a block in which most of

The UBA Domains of NUB1L Are Required for Binding but Not for Accelerated Degradation of the Ubiquitin-like Modifier FAT10

A version of NUB1L lacking all three UBA domains, on the other hand, looses the ability to bind FAT10 but is still able to interact with the proteasome and accelerates the deg-

Implicit learning leads to familiarity effects for intonation but not for voice

Results of two auditory lexical decision tasks (Experiment 1 with a task-based familiarization phase and Experiment 2 with a passive listening familiarization phase),