Recent content by Van Ladmon

But why Kleinert differentiates the two kinds of variations: ##\delta q## used in Hamilton's principle and ##\delta_s q## in Noether's theorem? He says that ##\delta_s q## need not be ##0## on the boundaries. Also, what do you mean by expressing everything in terms of "old coordinates"? Could...

In the derivation of energy conservation, there is the transformation ##q(t)\rightarrow q'(t)=q(t+\epsilon)##, whose end points are kind of fuzzy. The original path ##q(t)## is only defined from ##t_1## to ##t_2##. If this transformation rule is imposed, ##q'(t_2-\epsilon)=q(t_2)## to...

Homework Statement Is the following conclusion correct? Assume there's an equation with vectors on both sides. Taking the dot product of this equation with vectors on both sides loses information, but information will not lose when taking dot products with higher rank tensors on both sides...

It indeed looks like a bug but is there any relationship between PlotLegend and ChartLegends? ChartLegends work well in a chart when there's more than 5 of them.

I want to add legends in ArrayPlot and my code is like this: Table[ArrayPlot[ FiniteGroupData[{"CyclicGroup", i}, "MultiplicationTable"], PlotLegends -> Range[i], ColorRules -> {x_ -> ColorData["Rainbow"][(x/i)]}], {i, 1, 10}] In the first 5 graphs this work well, but after the 6th graph...

$$T_i^1 u^i v^2 w^3 + T_i^1 u^1 v^i w^2 + T_i^1 u^1 v^3 w^i=$$ \begin{equation*} \left.\begin{aligned} T_1^1 u^1 v^2 w^3 + T_1^1 u^3 v^1 w^2 + T_1^1 u^2 v^3 w^1 \\ T_2^1 u^2 v^2 w^3 + T_2^1 u^3 v^2 w^2 + T_2^1 u^2 v^3 w^2 \\ T_3^1 u^3 v^2 w^3 + T_3^1...

Many thanks for the hint and I've worked out this problem, but is there a more concise and elegant way to give out a proof using tensor calculus?

Homework Statement How to proof the following property of tensor invariants? Where: ##[\mathbf{a\; b\; c}]=\mathbf{a\cdot (b\times c)} ##, ##\mathbf{T} ##is a second order tensor, ##\mathfrak{J}_{1}^{T}##is its first invariant, ##\mathbf{u, v, w}## are vectors. Homework Equations...