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searching for Small-angle approximation 16 found (53 total)

alternate case: small-angle approximation

Quantum pendulum (1,016 words) [view diff] exact match in snippet view article find links to article

other quantum phenomena. Though a pendulum not subject to the small-angle approximation has an inherent nonlinearity, the Schrödinger equation for the

String vibration (2,042 words) [view diff] no match in snippet view article find links to article

which the net horizontal force is zero. Accordingly, using the small angle approximation, the horizontal tensions acting on both sides of the string segment

Tidal tensor (1,330 words) [view diff] no match in snippet view article find links to article

\phi } direction. Using some elementary trigonometry and the small angle approximation, we find that the force vectors differ by a vector tangent to

Nonlinear system (2,597 words) [view diff] no match in snippet view article find links to article

linearization at θ = 0 {\displaystyle \theta =0} , called the small angle approximation, is d 2 θ d t 2 + θ = 0 {\displaystyle {\frac {d^{2}\theta }{dt^{2}}}+\theta

Compound prism (1,727 words) [view diff] no match in snippet view article find links to article

\end{aligned}}} Note that this formula is only accurate under the small angle approximation. While the doublet prism is the simplest compound prism type,

Frame fields in general relativity (4,996 words) [view diff] no match in snippet view article find links to article

{\displaystyle r=r_{0}} . Using some elementary trigonometry and the small angle approximation, we find that the force vectors differ by a vector tangent to

Contrast transfer function (2,946 words) [view diff] exact match in snippet view article find links to article

proportional to the cube of the incident angle (θ) under the small-angle approximation, and that the explicit form in this case is r s = C s ⋅ θ 3 ⋅

Timeline of abelian varieties (1,038 words) [view diff] exact match in snippet view article find links to article

1736 Leonhard Euler writes on the pendulum equation without the small-angle approximation. 1738 Euler writes on curves of genus 1 considered by Fermat and

Cantilever magnetometry (950 words) [view diff] no match in snippet view article find links to article

similarly described by this differential equation and solution in the small angle approximation. We can use the binomial expansion to rewrite ω {\displaystyle

Geometrical optics (4,688 words) [view diff] no match in snippet view article find links to article

is often simplified by making the paraxial approximation, or "small angle approximation". The mathematical behavior then becomes linear, allowing optical

Relativistic images (2,043 words) [view diff] case mismatch in snippet view article find links to article

(2008). "THEORETICAL GRAVITATIONAL LENSING – BEYOND THE WEAK-FIELD SMALL-ANGLE APPROXIMATION". The Eleventh Marcel Grossmann Meeting. World Scientific Publishing

Neutrino oscillation (7,379 words) [view diff] exact match in snippet view article find links to article

not identical the analysis is slightly more complicated. In the small-angle approximation, the potential energy of a single pendulum system is 1 2 m g L

Optics (12,848 words) [view diff] no match in snippet view article find links to article

is often simplified by making the paraxial approximation, or "small angle approximation". The mathematical behaviour then becomes linear, allowing optical

Multislice (3,253 words) [view diff] exact match in snippet view article find links to article

π / λ {\displaystyle k=2\pi /\lambda } ). In the case of the small-angle approximation ( θ ∼ {\displaystyle \theta \sim } 100 mRad) we can approximate

Pendulum (14,432 words) [view diff] no match in snippet view article find links to article

(0.05 radians), the difference between the true period and the small angle approximation (1) amounts to about 15 seconds per day. For small swings the

Taylor–Maccoll flow (1,657 words) [view diff] exact match in snippet view article find links to article

and conesequently g ′ = U χ {\displaystyle g'=U\chi } . In the small-angle approximation, the weak shock cone is given by z = β ρ {\displaystyle z=\beta