# Doesn't linear motion include curvilinear and rectilinear motion?

From some Portuguese language textbooks, I learned the following definitions:

• linear motion (movimento linear): motion along a line;
• rectilinear motion (movimento retilíneo): motion along a straight line;
• curvilinear motion (movimento curvilíneo): motion along a curved line.

Judging by those definitions, it's clear that linear includes rectilinear and curvilinear, what seems logical when I look at the words, but it seems that, in English language Physics, linear motion is the same as rectilinear motion.

Should that difference be considered a simple linguistic difference? A divergence in how the original concepts evolved and were reinterpreted in each language? Or, contrary to what seemed to me, does linear also include recti- and curvilinear motions in English?

Edit:

It was said that a "linear motion" would be simply "motion" if defined the way I described. I think that's true if you have already restricted ourselves to the motion of particles, since the motion of solid bodies and fluids are not fully described as lines.

I should explain that I found that distinction in Portuguese in the context of uniform and uniformly varying motion. As the motion of a car moving on a road or a float in the stream of a river are usually nonrectilinear but might be considered as at approximately constant speed, the concept of uniform linear motion (constant velocity magnitude) is used instead of that of uniform rectilinear motion (constant velocity vector).

It seems that Brazilians use the expression uniform linear motion to refer to uniform curvilinear motion (the adjective "curvilinear" is rared used here) while English speakers use it to uniform rectilinear motion (I guess "rectilinear" is rarely used there, since it's a synonym of "linear" in practice).

• I think your first impression is right. However, sometimes we use the word 'line' the same way you do, e.g. a 'worldline' in special relativity may be curved. Most of the time, 'line' means 'straight line'. Jan 18, 2016 at 22:48
• Then there are linear dynamic systems of which the motions are not necessarily in a straight line. But in this case linear refers to the properties of homogeneity and superposition. More words to consider! Jan 19, 2016 at 0:04
• Huh, your edit is interesting. For some reason, it always seems like physics in non-English has tons of extra, mildly 18th century sounding terms... how in the world do you remember all these words? Jan 19, 2016 at 1:38
• @knzhou Well, besides that "linear motion" thing, I can't recall other extra Physics terms in Portuguese language, compared to English. Come to think of it, the translations in practice are pt. "linear": en. "curvilinear", pt. "retilíneo": en. "linear". Althought our "linear" rigorously includes "retilíneo", it's mostly used to take into consideration that the motion is not along a straight line. Jan 19, 2016 at 16:26
• @knzhou With regard to vectors, it's English that apparently has more terms than Portuguese. In Portuguese, a vector has direção for English "orientation" and sentido for English "sense", but no word for English "direction", which encompasses "orientation" and "sense". Jan 19, 2016 at 16:32

As a native English speaker, I don't even see three definitions. The first two sounded 100% the same all the way up until you wrote the third. At which point the first one sounded pretty meaningless. You could just say motion if you meant any possible motion.

To do science we have to make predictions. Which means you predict that one thing happens as opposed to a distinguishable alternative.

What is the alternative to linear motion. If you've expanded the word line to mean curve (which happens when we speak of worldlines in relativity) then what is the alternative? Teleportation? Being in multiple places at once?

You can break motion subcollections called planar motion and linear motion where linear motion is motion confined to a (straight) line and planar motion is motion confined to a (flat) plane respectively. And when it isn't either of those it is still motion, so you also have more general motion. And I'm even OK with motion including being stationary.

But this breakdown into clear categories where you can tell which is included in which is the real key issue. I'm used to seeing general motion, motion that stays in a plane, and motion that stays in a line and being at rest. And it's nice to know when one is more general than the other.

But trying to get line or curve to sound more general than the other is not going to be a win in the short term. And you can just say motion is you want to cover motion whose path is curved or straight.

Context can get you to think one (curve or line) is more general in a specific context. For instance a worldline can be curved, and a curve could be a function from an interval of real numbers into a manifold (a function whose image might be a straight line). But really we use both. So a worldline is actually a curve, a differentiable curve with timelike tangent vectors.

• Huh, I agree with your first comment. What would 'nonlinear' motion even be? Jan 18, 2016 at 23:51
• I just edited the question to explain how "linear" might be distinct from "rectilinear" and still significant. Jan 19, 2016 at 1:38