188
2 Variational Problems with Fixed Boundaries
Integrating the above equation gives
θ =
c 1 dr
r
ln
2 r − c
2
1
=
c 1 d ln r
ln
2 r − c
2
1
= c 1 ln(ln r +
ln
2 r − c
2
1 ) + c 2
or
θ = c 1 arccosh(ln r ) + c 2
2.11 Introduction to the Famous Scientists
Galilei (Galileo, 1564.2.15–1642.1.8) Italian physicist, astronomer, philosopher and
mathematician, one of the founders of rational science and modern experimental
science. Born in Pisa, died in Arcetri. In 1581–1585 studying medicine and physics at
the University of Pisa. Served as a professor at the University of Pisa in 1589. Served
as a professor at the University of Padua in 1591. Became a fellow of the Lincean
Academy in 1611. Through the experiment, Overthrew the theory of Aristotle about
falling body down speed being proportional to the weight, established the law of
falling body. Also found the law of inertia of the object, the isochronism of pendulum
vibration and the motion law of projectile, and determined the Galileon principle of
relativity. Discussed the material’s strength in his mechanical work and created material science. He was the first person using the telescope to observe celestial bodies
and obtain lot of achievements. In the discovery of astronomy effectively proved the
Copernican heliocentric theory. The works had Dialogo sopra i due massimi sistemi
del mondo (Dialogue Concerning the Two Chief World Systems, 1632) and Discorsi
e Dimostrazioni Matematiche intorno a due nuove scienze (Dialogues Concerning
Two New Sciences, 1638) etc.
Huygens (Christiaan, 1629.4.14–1695.7.8) Dutch mathematician, physicist and
astronomer. Born and died in Hague. Studying at the University of Leiden in 1645,
two years later transferred to the Breda University to study. Received doctorate in
law from the France University of Angers in 1655. Became the first foreign member
of the Royal Society in 1663. Became a member of the French Academy of Sciences
in 1666. The main contribution to mathematics was that he promoted the research of
infinitesimal analysis and its applications, promoted the formation and development
of the theory of probability. Had an intensive research for a variety of curves, obtained
a series of important achievements, proposed the concepts of evolute and asymptote, gave the formula of radius of curvature, proved the cycloid is an isochronous
curve, etc. The most important contribution to astronomy was that he discovered
the Saturn’s rings and Titan. The main contribution to physics was that he founded
the wave theory of light. Had important improvement to the telescope, improved the
clock controlled by the pendulum. The works had Horologium oscillatorium sive
2 Variational Problems with Fixed Boundaries
Integrating the above equation gives
θ =
c 1 dr
r
ln
2 r − c
2
1
=
c 1 d ln r
ln
2 r − c
2
1
= c 1 ln(ln r +
ln
2 r − c
2
1 ) + c 2
or
θ = c 1 arccosh(ln r ) + c 2
2.11 Introduction to the Famous Scientists
Galilei (Galileo, 1564.2.15–1642.1.8) Italian physicist, astronomer, philosopher and
mathematician, one of the founders of rational science and modern experimental
science. Born in Pisa, died in Arcetri. In 1581–1585 studying medicine and physics at
the University of Pisa. Served as a professor at the University of Pisa in 1589. Served
as a professor at the University of Padua in 1591. Became a fellow of the Lincean
Academy in 1611. Through the experiment, Overthrew the theory of Aristotle about
falling body down speed being proportional to the weight, established the law of
falling body. Also found the law of inertia of the object, the isochronism of pendulum
vibration and the motion law of projectile, and determined the Galileon principle of
relativity. Discussed the material’s strength in his mechanical work and created material science. He was the first person using the telescope to observe celestial bodies
and obtain lot of achievements. In the discovery of astronomy effectively proved the
Copernican heliocentric theory. The works had Dialogo sopra i due massimi sistemi
del mondo (Dialogue Concerning the Two Chief World Systems, 1632) and Discorsi
e Dimostrazioni Matematiche intorno a due nuove scienze (Dialogues Concerning
Two New Sciences, 1638) etc.
Huygens (Christiaan, 1629.4.14–1695.7.8) Dutch mathematician, physicist and
astronomer. Born and died in Hague. Studying at the University of Leiden in 1645,
two years later transferred to the Breda University to study. Received doctorate in
law from the France University of Angers in 1655. Became the first foreign member
of the Royal Society in 1663. Became a member of the French Academy of Sciences
in 1666. The main contribution to mathematics was that he promoted the research of
infinitesimal analysis and its applications, promoted the formation and development
of the theory of probability. Had an intensive research for a variety of curves, obtained
a series of important achievements, proposed the concepts of evolute and asymptote, gave the formula of radius of curvature, proved the cycloid is an isochronous
curve, etc. The most important contribution to astronomy was that he discovered
the Saturn’s rings and Titan. The main contribution to physics was that he founded
the wave theory of light. Had important improvement to the telescope, improved the
clock controlled by the pendulum. The works had Horologium oscillatorium sive